The Squares Project

The square packing problem is a simple and long-standing problem in geometry: what is the size of the smallest square that can hold $n$ unit squares, where the squares are free to rotate but cannot overlap? The side length of that smallest square is written $s(n)$.

The question of the value of $s(n)$ is simple, but the answer is an open problem for most $n$. In many cases, $s(n)$ is known only to lie between an upper bound (the size of the enclosing square for the tightest packing ever discovered, such as $s(29) \le 5.934$) and a lower bound (a size below which it is proved that no packing can exist, such as the reported $s(29) \ge 5.81$).

The project covers the problem at every $n$. Its frontier keeps one record for each case $n = 1\ldots324$, with reported and verified bounds kept separate, and its results register grades each registered result, this project’s or another’s, by how far it has been checked. It goes into most depth where there is recent progress, which in September 2026 means $n = 11$, $n = 17$, and the exact values newly proved at $n = 21$, $32$ and $45$. At seventeen squares both ends of the bracket are now machine-checked: Guzhou0806’s lower bound $s(17) > 4.66044275$ (T-093), and the upper bound $s(17) \le 4.67553009\ldots$ of John Bidwell’s 1998 packing, certified exactly from Kleddamag’s rational witness (T-065).

A recent major result settles eleven squares, until then the smallest case still open: $s(11) = T = 3.877083590022814\ldots$, the exact side of Walter Trump’s 1979 packing. T-060 records the global lower bound from the Astra-assisted 11SquaresOptimal proof by Mannaseh Ahmed, building on this project and Kleddamag. This repository independently replayed the proof’s exact inputs and audited their mathematical composition (V3/C3/S5: machine-checked, review record pending); T-011 verifies Trump’s matching witness. The same argument, read at side exactly $T$, shows that Trump’s packing is the only optimal one up to the eight symmetries of the container and relabelling of the squares: T-112 registers that direct corollary of T-060, which adds no computation (V3/C2/S3: its step at side $T$ is prose). The case record, review, and retained packet state what the confirmation depends on and the reproducibility defects found in the source. On 6 October 2026 the proof was announced as formalized in Lean 4 “thanks to Astra and Claude”, in 11SquaresFormalized by Mannaseh Ahmed and contributors. This project’s statement audit reads its theorem as exactly $s(11) = T$, and its source reports that its full verification run, resumed from earlier validated receipts, passed, trusting Lean’s compiler for its numerical certificates. It is recorded on T-060 as the source’s report; a complete build this record can rest on, and a human expert’s review of the formalization, are still to come.

The results live on the project site, Square Packing. It carries the recent results by this project and by others with their credit, the verification ratings, the atlas of known-best packings and its films, the table of every result, and the frontier survey of every case $n = 1\ldots324$, all generated from the record in this repository. The in-repository record is the results register, the per-case status table, and epistemics.md, which defines how each claim is graded. The site and the atlas posters are at edition v0.5.0; each paper carries a version of its own; the atlas films are the ones cut for the v0.4.2 release.

The site’s papers explain constructions, search methods, and proofs. Three of them form one series on $n = 11$, read in order:

1. New Lower Bounds for Square Packing for n = 11: how weighted points and 2-of-3 threshold atoms prove T-018, T-025 and T-026, $s(11) \ge 3.8264\ldots$, with interactive figures (PDF, source).
2. A Review of the Certified Lower Bound s(11) > 31/8 for 11 Squares: explains Kleddamag’s proof that $s(11) > 31/8$ (T-037): five-site k-of-m charges, k-of-m charges on shrunken parents with strict cores, and a reoptimized certificate over 12,028 angle rows (PDF, source).
3. A Review of the Optimality Proof of the Trump Packing of 11 Squares: explains Ahmed’s proof that Trump’s packing is optimal, $s(11) = 3.8770835\ldots$ (T-060): construction, case exclusions, capture and local isolation, with figures drawn from or checked against the retained proof data (PDF, source).

For how record packings are found, read How Record Square Packings Are Found, a tutorial on geometric construction, physics-inspired search, annealing, surgery, local refinement, and upper-bound certification (PDF, source).

This repository also contains a set of tools and AI workflows for automated mathematical research: the results and the frontier survey are produced and checked by AI agents running a recorded process, with hypotheses registered before measurement, every claim graded, and every defect logged. The rest of this README is about that work.

Results (site) · Research Status · Repository Guide · Getting Started · Reports · Autonomous Research Process · Conventions · Layout

Repository Guide

Where	What
Tutorial	First-principles introduction to the objects, bounds, cells, stationary branches, search, and proof obligations
How Record Packings Are Found	Geometric construction, physics-inspired search, annealing, surgery, local refinement, and upper-bound certification, with sourced record histories
Synopsis	Current research status and roadmap, established results, terminology, workflow contracts, and handoff
Results register	Whole-result bounds, audits, structural theorems, and errata graded under epistemics.md
Frontier	One record per case for $n = 1\ldots324$, with reported and verified bounds kept separate
Atlas	Known-best and prospective packings, contact-scaffold enumeration, and deterministic renderings
Literature	Retained primary sources, cleaned transcriptions, raw extractions, and the maintained index of upstream repositories we integrate from
Reports	Research reports on the mathematics, algorithms, infrastructure, formal proof, and search strategy
Code and development guide	Exact verification, search, promotion, the verification tooling overview of what the checkers cover, and the validation tiers and behavioral lanes that gate every change
Campaign record	Hypotheses, preregistered experiments, session records, agendas, and generated ledger
Defect log	Generated record of defects, detection methods, fixes, and regressions

Long-lived tests and runs retain detailed timing evidence under OR-14. The validation efficiency and checkpoints plan tracks improvements to everyday feedback and full final checkpoints, with measurements and preserved coverage required before accepting a speedup.

SYNOPSIS.md is the technical root and current-state document. Its research-status roll-up synthesizes the generated frontier status table, results register, campaign ledger, agenda map, and session close report. The W8 documentation pass defines how those sources are reconciled. The separate small-n mathematical audit challenges the current research approaches and supplies the enlarged candidate set. The subsequent W10 route-selection review derives the due efficiency checkpoint, records every candidate’s disposition, and separates the next W5 block from the later scientific choice. To resume work, use the synopsis’s current handoff, which names the owning work item and next bounded slice.

Getting Started

Read TUTORIAL.md once for the mathematical orientation, then the synopsis’s research status and roadmap for current results and open work. Run commands from packing/; the project uses Python 3.14 through uv.

Essential Terminology

These are the terms a reader encounters most often. The synopsis terminology gives the full definitions.

Term	Meaning
configuration	A placement of all $n$ squares plus the container side: $3n + 1$ coordinates
cell	A separating axis and order for every pair of squares; with angles fixed, one cell is one linear program
quench	Deterministic refinement from a configuration to a local optimum
basin	The preimage of one returned pose under a fixed deterministic quench; one connected terminal component may contain several point-basins
polish	Refinement within the current basin
exploration	Work intended to reach a different basin; the term implies no assurance level
standing best	The best published side for that $n$, hence an upper bound rather than known optimality in open cases
gap	best_side − standing_best, always signed
assurance	reported, numerically-checked, or verified; method, arithmetic, origin, limitations, and novelty are recorded separately

Essential Conventions

One ID names one durable thing, and IDs are not reused. The prefix identifies the record’s layer; conventions.md is the definitive registry.

ID	Names
n-NNN	One frontier case, such as n-011
T-NNN	One whole result in the results register; the synopsis also has older local T-N shorthand
X-NNN	One exploration report from which hypotheses may be derived
H-NNN	One falsifiable hypothesis or open question
exp-NNN	One durable experiment record; a lower-level run is one command invocation or seed trial
series-NNN	One campaign-wide tooling and comparability regime
agenda-NNN	One ordered queue of bounded commitments
BC-NNN	One bounded commitment in an agenda; other agendas may declare another two-letter prefix
session-NNN	One escalated agent-session record containing ordered workflow phases
D-NNN	One defect and its detection, consequence, fix, and regression
think-xxxx	One git-native tbd bead: durable work and dependency state
W1–W10	A workflow entry point, not a durable artifact ID

Other rules needed to read the repository:

• Structured values live in YAML or frontmatter; prose supplies explanation and judgment. A consumer does not scrape prose for fields.
• Declared paths are repository-relative. Generated views are regenerated from their source records and are not edited by hand.
• Evidence assurance, method, origin, precision, limitations, and novelty are separate facts. Whole-result V/C classifications do not replace evidence-level fields.
• Source-faithful archive material is not cleaned up as project prose. Reconstructed source text is marked and counted.
• Corrections preserve the original record and add a dated statement of what remains valid. IDs and scientific outcomes are not silently rewritten.

Technical Stack

The project keeps numerical exploration, symbolic reconstruction, exact verification, and research records as separate layers.

Layer	Tools	Role here
Work and issue state	tbd	Git-native beads, dependencies, specs, guidelines, and handoffs
Structured research records	softschema, PyYAML, Python jsonschema, and jsonschema-rs	Mixed prose-and-data artifacts, JSON Schema contracts, in-process checks, and fast repository-wide validation
Documentation	Flowmark and Practical Prose	Semantic Markdown formatting and the common documentation guidelines
High-precision numerics	mpmath	Arbitrary-precision refinement, interval endpoints, and decimal-to-exact promotion
Arrays and optimization	NumPy and SciPy	Geometry arrays, nonlinear refinement, and fixed-cell linear programs
Symbolic mathematics	SymPy	Contact-system assembly, elimination probes, minimal-polynomial recovery, and independent symbolic checks
Exact mathematics	sqpack.field, sqpack.verify, and the case-specific certifiers	Rational and algebraic sign decisions, unavoidable-set certificates, Krawczyk enclosures, and proof replay
Parallel search	The local sqsearch crate, Rayon, and the Rust toolchain	Multicore f64 screening and annealing; formal promotion remains on the Python side
Python environment and QA	uv, Ruff, BasedPyright, and pytest	Locked environments, linting, formatting, type checking, and behavioral tests
Git hooks	lefthook	Runs the pinned Markdown formatter and re-stages its changes before commit

The dependency and tool versions are owned by packing/pyproject.toml, packing/uv.lock, packing/sqsearch/Cargo.toml, and the root Makefile and hook configuration. development.md explains how the layers interact.

Core Commands

uv sync --frozen --all-extras --group dev
uv run --frozen packing-witness inspect witnesses/schadt-n029-2025-decimal.yaml
uv run --frozen packing-witness check witnesses/schadt-n029-2025-decimal.yaml \
  --method numerical-multiprecision --precision 300 --tolerance 1e-100
uv run --frozen packing-witness verify witnesses/schadt-n029-2025-rational.yaml
uv run --frozen python -m cases.trump11.verify_exact
uv run --frozen --all-extras --group dev packing-validate --edit

--records, --edit, --push, --fast, and the full checkpoint are the five lifecycle tiers. --edit is the ordinary inner loop; pull-request CI executes --fast as seven disjoint required parts. Which steps each tier runs, what it costs, and which of the three behavioral lanes a test lands in are tabulated in development.md → Validation Loops; the ceilings themselves are data the gate reads, in packing/devtools/gate-budgets.yaml. In short: a contributor runs --edit while editing and --push before pushing, every pull request runs all seven parts of --fast, and the complete gate runs on main and at the end of a research block.

Witness/v2 is the interchange format for supported rational, algebraic, and decimal witnesses. Exact verification covers rational witnesses and algebraic witnesses whose field preconditions the tool can certify. Recovering exact geometry from arbitrary decimal input remains the hard step; development.md and the module docstrings under packing/src/sqpack/ define the supported APIs and limits.

sqpack.render creates deterministic, self-contained SVG figures while preserving the input’s evidence tier in captions and metadata. The rendering guide owns the CLI, gallery, contact annotations, portability contract, and Motion Lab. The Motion Lab is an exploratory instrument, not a citable research result.

Reports

These 40 research reports are the durable topical syntheses:

Report	Scope
n17 Restricted Family-Cell Audit	Exact replay forces the free square into side-S2 for a fixed sixteen-square endpoint skeleton on a restricted slider box; no perturbed-core capture or global exclusion
n17 Shared-Centre LP Readiness	Prospective first-eight shared-centre pilot, exact endpoint feasibility control and bounded certificate contract; no LP implementation or result
Owned-Core Guarded Clauses	Transport of the verified same-core implication to a polynomial pose guard, with endpoint disjointness and the complementary-cover obligation separated
Case-Preserving Owned Propagation	Verified regional orientation gain, retained case correlations and the next simultaneous propagation contract
n11 Envelope Transfer	Whole-square containment windows transferring the settled n11 bound, with complete finite positive and negative checks
Normalized Contact Rank Filter	Hand forest/capacity relaxation for full-rank representatives, exact rejection-certificate contract and a bounded prospective 95-orbit discriminator
Global Contact Budget for n17	Hand normalization proof requiring at least 19 distinct pair contacts and three graph cycles; finite arithmetic checks and global capture remain separate obligations
Two-Child Collective Propagation	Two closed regional centre cases and a verified additional 15/32 orientation restriction measured after their surviving-case union
One-Round Owned-Domain Propagation	Complete one-round ownership recovery and collective restriction contract on accepted guarded geometry
Strict Core Regional Transfer	Freshly checked 25-row conditional restriction at radius $2^{-23}$ in exp299; direct reconstruction at radius $1/512$ retains 22 rows in exp297
n17 Session 186 W3 Strategy	Positive-width regional lifting, conditional propagation and measured verification priorities for the six-hour continuation
Full-square partner coupling	Prospective exact separating-axis test and a positive-margin lift to a closed nonzero region
Complete Partner-Pose Coupling for the n17 Parent	Complete-row collision quantifiers, the fixed-witness discriminator, closed-region ladder and endpoint-family safeguards
n17 W3 Capacity and Route Selection	Global capture versus replay bottlenecks, the accepted reduced-model witness, prioritized coupling and optimization blocks, and conditional alternatives
n17 Proof Interfaces and Finite-Angle LP Contract	Conditional fixed-container proof joins, finite-angle branch semantics, exact feature/apex/patch contracts, and remaining global capture obligations
Publishing GitHub Work from Codex Cloud	Diagnosis of GitHub access in Codex Cloud, the verified publication repair, and reusable setup and validation evidence
Cloud Intake State Checkpoint	Completed SQUISH publication, pending second-update validation, retained preparation archives, and the open intake queue
s(12) Beyond Rescaling	Daniel’s s(12) certificate scaled past #309 at a finer angle net, then re-weighted by linear programming to a candidate s(12) ≥ 15680000/3949423, with source-verifier receipts and controls
Where the Authors’ Measure Checkers Spend Their Time	Function-level profiles of Tokoharu’s and wand125’s outward-rounded checkers on one certificate per family, and what they imply for an independent verifier; withheld from that verifier’s clean-room implementers
Exact Arithmetic for Independent Verifiers	Source-level comparison of Python and Rust rational arithmetic, native-library options, sampled profiles, and a controlled experiment measuring redundant normalization
Fractional Packing, Duality, and the Next N11 Discriminators	Exact full-unit transport, interior duality and density equivalence, finite witnesses, and the limits of fractional obstructions
Seven Corner Marks, Contact Components, and Relational Helpers	New ownership and contact-component deductions, shared-owner consistency, and bounded segment-helper comparisons
Certificate Mechanisms After the N11 Fractional Ceilings	Recent bound gains, weighted and floor charges, geometric expressiveness tests, and the finite optimal-dual-face criterion
N11: The Missing Owner-Selection Theorem	Exact owner-selection obligation, sixteen avoiding products, wall-chart symmetry split, proved path bounds, narrow four-parent controls, and two proposed surplus tests: the T1 bottom-left role-C inequality was rejected by exp-157; T2 remains unrun
BC303 Literal Parent-Union Mass	Exact Q0 mass and independent four-corner replay; both frozen necessary resource tests survive with 1,048,233 source units of slack, without an extension or global conclusion
BC303 T2: From the Accepted Pose Domains to Exact Charge Tests	Accepted C open-cell reduction and S first-owner sufficient test, with exact sweep and witness conditions; no charge or T2 verdict
N11 Definitions, Findings, and the Inference Chain	First-principles interpretation through exp153, exact scope of results, remaining proof obligations, and unranked alternatives
N11 Inference Audit	Corrections to overbroad summaries, physical-versus-relaxed quantifiers, and missing evidence
Packing 11 Unit Squares in a Square	Dated account of the former $s(11)$ gap and earlier proof techniques; T-060 and the current case record supersede its status summary
Algorithms and Tooling for Square Packing	Search, numerical-to-exact promotion, verification, and the record landscape
FrankenSim as a Rust Toolkit for Square Packing	Assessment of certified-arithmetic and determinism components in a larger Rust framework
Infrastructure for Square-Packing Exploration	Build order, latency tiers, language boundaries, and symbolic tooling
Lean for Square-Packing Proofs and Validation	Where proof assistants fit and which certificate layers are suitable first targets
A Search Philosophy for Square Packing	Basin cartography, structural diversity, relaxation ladders, and search strategy
Public Sources Beyond n = 100	Which catalogues carry geometry above 100, their reuse terms, and why 324 is a source boundary
Stromquist’s 1984 Memos and Systematic Dots Proofs	Historical corrections, the three memo arguments, and a reusable conditional counting control
Annealing for Square Packing, and How Far It Actually Reaches	What “solve to $n = 100$” actually asks for, what the record engines do, and why the move set rather than the cooling schedule is the binding constraint
Physics and Simulation Mechanisms for Square Packing	Inflation, shrinking cells, constraint projection, contact solvers, smoothing continuation and differentiable simulation, and which of them could recover a record cold
Stromquist’s Twenty-Six-Square Packing	Exact verification, comparison with the current record, source attribution, and bounded follow-up
The Best-Known n = 26 Packing	Dated literature and source search, exact score normalization, and the limits of the best-known claim

The reports distinguish formal proof, finite numerical checks, and source reports. The draft X-031 floor-normalized T2 exploration records reviewed local cutoffs and bounded H-161 stability; it establishes no target result or global bound. The document map identifies every maintained guide, dated record, generated view, and superseded document.

Autonomous Research Process

The repository supports autonomous research without making process a substitute for evidence. This section gives the operating model at a glance. The operating rules, workflow contracts, and campaign runbook own the full rules.

Assurance and Verification

Evidence uses three assurance labels:

• reported for a named source claim not checked here;
• numerically-checked for finite-precision calculations with their precision, rounding, and tolerance recorded; and
• verified for an exact check, rigorous interval certificate, or complete proof that covers the claim and its preconditions.

Whole results use the separate V/C classifications in epistemics.md. A verified feasible witness proves an upper bound; it does not prove global optimality without a matching verified lower bound.

Finite precision is not enough for a packing with exact contacts. Floating-point arithmetic can establish a strict positive gap, but a tolerance that accepts a true zero-gap contact also accepts a smaller overlap. Exact algebraic signs or outward-rounded intervals are therefore required before a contact-heavy witness becomes formally verified. The synopsis explains the full argument in Why Exactness Is Not Optional.

Two retained examples show the boundary. The Schadt $n = 29$ decimal pose passes its declared 300-digit numerical check, while the separately promoted interval witness establishes a slightly weaker side rigorously. Trump’s $n = 11$ witness is verified exactly over a degree-eight number field, including fourteen zero-gap contacts. The per-case records (n = 29, n = 11) state exactly which bound each artifact proves.

Verification answers whether a proposed packing is valid. Proving it optimal is a different problem and requires a matching lower bound. The synopsis’s capability ladder distinguishes what is built, what is ordinary engineering, and what remains mathematically contingent.

Operating Principles

Principle	Focus	Goal
Correctness	Soundness	Formal validation that third parties can inspect, plus cross-validation of claims and source summaries
Process	Discipline	The minimum effective structure that keeps consequential decisions, evidence, and handoffs reconstructible
Insight	Creativity	Freedom to understand the problem, form varied hypotheses, and use all available information and tools
Efficiency	Infrastructure	Faster iteration through measured improvement of algorithms, systems, tools, and research surfaces

Correctness is the veto: no result advances beyond its evidence, however costly the required check may be. Process is proportional infrastructure, not a second mathematical standard; missing evidence can block promotion, while a preferred form or checkpoint cannot block useful work merely because it looks more disciplined. Insight remains free to propose. Efficiency may simplify process but cannot lower the assurance bar.

Layers of Work

The system separates the kind of effort, the lens used to judge it, and the bounded action being executed:

Layer	Question	Recorded as
Operating principle / focus	What quality dimension is preeminent for this phase?	correctness, process, insight, or efficiency
Workflow	What durable result is this phase meant to produce?	One of W1–W10, or the narrow maintenance fallback
Slice	What bounded action is being performed now, and how will it be checked?	Objective, intended artifact, focused validation, and stop condition

Focus and workflow are independent. A W6 experiment may emphasize correctness, insight, or efficiency without changing its promise to execute a preregistered measurement; an efficiency-focused phase does not become W5 unless its durable result is a measured performance decision. A slice is smaller than either: it is one action inside the declared phase.

The durable work objects also have different lifetimes:

Unit	Lifetime and role
Packing exploration	The self-contained repository: sources, research, code, records, and tools
Campaign	The multi-session research program and its shared record contract
Series	A campaign-wide tooling regime and comparability boundary
Bead (think-xxxx)	A durable work item and dependency node, open until the work is settled
Bounded commitment (BC-NNN)	A planned attempt with entry conditions, acceptable exits, owner, and budget
Agent session	An escalated interval of coordinated work containing one or more workflow phases
Workflow phase	One declared purpose and focus within a session
Slice	One bounded, immediately checkable action within a phase
Exploration / hypothesis	A recorded source of ideas / one falsifiable claim with its criterion fixed before measurement
Experiment / run	One durable measured round / one lower-level invocation or seed trial
Result / ledger	One typed observation or whole-result claim / a generated view over source records

A bead says what needs doing. A bounded commitment says what would count as settling one attempt. A workflow phase says what kind of move is being executed now. One bead may require several commitments, one commitment may span several phases, and one phase may produce zero or several scientific records. The work-unit definitions, campaign runbook, and agent-session guide own the exact contracts.

Workflow Entry Points

Choose the workflow whose durable result matches the task. The synopsis owns the complete entry, exit, and transition contracts.

ID	Workflow	Enter when	Durable result	Usual handoff
W1	research-survey	The sourced state of knowledge is incomplete, or someone else has reported a result	A pinned source packet, claim IDs, proof obligations, source notes, conflicts, and explicit gaps; a reported result registered as reported	W2
W2	factual-review	Existing claims need efficient confirmation and a correctness audit	Focused proof receipts, explicit unresolved obligations, measured cost, and findings; for an imported result, its derived rungs; no new theory smuggled into the review	W5 for bottlenecks; W3 or W4 otherwise
W3	insight-iteration	Current evidence needs new explanations or hypotheses	Candidate X-NNN/H-NNN items with mechanisms, falsifiers, and information value	W6
W4	process-review	Work is hard to reconstruct or the discipline itself needs review	Process findings, beads, and narrowly scoped contract or check changes	W5 or the next owning workflow
W5	efficiency-loop	A measured bottleneck limits useful iterations	A baseline, profile, equivalence-safe change, and measured decision	Return to the originating workflow (W2, W6 or W7)
W6	research-loop	A registered hypothesis has a fixed criterion, regime, budget, and instrument contract	A frozen instrument and one or more exp-NNN records, raw evidence, verdicts, and a current ledger	W2 for promoted or high-risk claims; otherwise W3 or another W6 slice
W7	pipeline-improvement	A named packing-pipeline surface or research consumer needs a new, stronger, simpler, or repaired capability	A bounded implementation or refactor, executable controls, explicit evidence limits, cost receipt, and readiness decision; no scientific verdict	W2 before a materially changed trust boundary reaches W6; otherwise W5 or W6
W8	documentation-pass	A period of research has left the reader-facing documents behind what the record now says, or a confirmed result warrants a review paper	Reconciled root documents—README, tutorial, synopsis—checked against the artifacts and against each other, with every drift either fixed or logged as a defect, or a review paper with its exposition review; no new claim introduced	W2 for any claim the pass could not verify; otherwise the next owning workflow
W9	remediation	Confirmed defects or issue backlogs need a systematic repair wave	Risk-ranked dispositions, bounded repairs, regression checks, updated defect records, and rerouted blockers; no scientific verdict	W10
W10	review-planning-oversight	An agenda or consequential session has ended and its results must change the plan	Result and stop-reason classifications, actionable dispositions, reader-document review, a reprioritized candidate set, and one selected next entry	The selected workflow; W9 or W8 when remediation or documentation work wins

A result published by others follows the result import process, a standard sequence of these phases, whichever source delivers it: an issue, an owner’s message, a catalogue, or a watched repository. When the owner asks for an intake pass, make intake sweeps every source at once.

Use general-improvement only for repository maintenance that fits none of W1–W10. Routine work records a workflow, bounded objective, intended artifact, and focused check. Use a versioned agent-session record only when work crosses multiple workflow phases, coordinates independent delegates, or needs durable recovery state.

Defects and Corrections

defects.md is generated from packing/defects.yaml. It records every known defect in this toolchain, what caught it, the consequence, the correction, and the regression that now guards it. Two lessons govern review:

• Results that look unusually good receive the strongest challenge because many soundness defects have pointed in that direction.
• The automated gate checks only rules someone encoded. No soundness defect in the log was caught by it.

Current counts and detector statistics belong only in the generated defect log and the synopsis defect section. Corrections follow conventions.md §7: preserve the original record, add a dated correction that states what remains valid, and route any changed conclusion to the artifact that owns it.

The Autonomous Work Loop

W6 is the measured experiment loop rather than an umbrella for every session:

W3 insight iteration → registered hypothesis → W6 measured round → evidence and verdict
          ↑                                                        │
          └──────── successor questions ← W2 factual review ←──────┘

The hypothesis, criterion, regime, budget, and stop rule are fixed before measurement. The round records every outcome and stops at the criterion or clock. Promoted, novel, disputed, or otherwise high-risk claims receive an independent W2 pass before they move forward; routine rounds whose recorded guards already decide the criterion may return directly to W3 or another W6 slice.

The tbd queue owns durable work and dependencies. Campaign agendas order bounded commitments; hypothesis and experiment records own scientific claims and measurements; commits own code; escalated agent-session records own phase and recovery state. The key record IDs are X-NNN for explorations, H-NNN for hypotheses, exp-NNN for experiments, BC-NNN for bounded commitments, T-NNN for registered results, and D-NNN for defects. conventions.md owns the complete ID registry.

The campaign’s bounded research cycle defines clocks, result routing, budgets, and stop rules. Changing agents changes the driver, not the record or the evidence required for a claim.

Where the Contracts Live

Document	Definitive responsibility
This README	High-level orientation and the relationship among the layers
SYNOPSIS.md	Current research status and roadmap, technical state, workflow contracts, work-unit vocabulary, and handoff
epistemics.md	Whole-result V/C/S/N classifications and their executable boundary
conventions.md	IDs, filenames, artifact shape, evidence fields, provenance, and corrections
operating-rules.md	How sessions choose, divide, validate, and hand off work
Campaign runbook	Hypothesis and experiment mechanics, clocks, budgets, verdicts, and routing
Result import process	Importing, recording, validating, rating and publishing a result by others, and answering its author
W8 documentation pass	Source-first reader-document reconciliation and the checked synopsis roll-up
W9 remediation pass	Systematic defect and issue-backlog triage, repair waves, and terminal dispositions
W10 review, planning, and oversight	Post-agenda result classification, document review, reprioritization, and next-entry selection
Agent-session guide	Escalation threshold, workflow phases, recovery state, and session closeout
Agendas	Mutable ordering and readiness of bounded commitments
development.md	Engineering boundaries, commands, tests, and validation tiers

Conventions

conventions.md owns identifiers, filenames, artifact discipline, evidence fields, provenance, corrections, and the boundary between machine checks and review. epistemics.md owns whole-result classifications and the policy for results by others: their scope, credit, import and reply. operating-rules.md owns how sessions are conducted, and development.md owns the engineering and validation workflow.

Layout

.
├── TUTORIAL.md             First-principles orientation for a newcomer
├── SYNOPSIS.md             Current research status, roadmap, results, and handoff
├── conventions.md          Artifact, identifier, evidence, and correction rules
├── epistemics.md           Whole-result verification and confirmation rubric
├── operating-rules.md      Session conduct and workflow rules
├── development.md          Python setup, engineering boundaries, and validation
├── defects.md              Generated view of packing/defects.yaml
├── docs/project/           Reports, reviews, specs, postmortems, and dated handoffs
├── docs/project/research/  The research reports listed above
├── packing/                Code, data, and the research record
│   ├── campaign/           Hypotheses, experiments, sessions, agendas, and ledger
│   ├── frontier/           Per-case claims, evidence, generated views, and results
│   ├── witnesses/          Witness/v2 interchange and retained examples
│   ├── golden/             Calibration endpoint snapshots
│   ├── atlas/              Known-best, prospective, enumerated, and rendering artifacts
│   ├── resources/          Retained literature and source-faithful transcriptions
│   ├── src/                Maintained sqpack package
│   ├── cases/              Case- and theorem-specific retained code
│   ├── devtools/           Checkers, adapters, generators, and mutation controls
│   ├── benchmarks/         Explicit performance probes
│   ├── tests/              Behavior, command, and architecture contracts
│   ├── sqsearch/           Rust screening annealer
│   ├── defects.yaml        Structured defect log
│   ├── defects.schema.yaml Defect-log contract
│   └── frankensim-probe/   Focused experiments against FrankenSim
├── packages/workbench/     Typed workbench source, tests, probes, and build tools
├── vendor/kpress/          Vendored kpress submodule: the page's rendering layer
├── AGENTS.md               Project instructions for agents
├── CLAUDE.md               Bridge to AGENTS.md
├── Makefile                Markdown formatting, hooks, and skill mirroring
├── biome.json              Biome lint and format config for the browser sources
├── eslint.probes.json      Type information for the probe promise-rule overlay
├── lefthook.yml            Pre-commit Markdown formatter hook
├── package.json            Pinned tooling and private npm workspace declaration
├── package-lock.json       Root and workbench workspace lockfile
├── tsconfig.base.json      The shared TypeScript type floor every program extends
├── tsconfig.devtools-node.json  The Node scripts the Python devtools and tests run
├── tsconfig.n11-lower-bounds-explainer.json The checked classic scripts in the standalone explainer
├── tsconfig.json           The bundled workbench application's entry module
├── tsconfig.motion-lab.json  The motion lab's assets and the slideshow harness
├── tsconfig.overview.json  The site pages' table and math scripts
└── tsconfig.probes.json    The workbench checkers' probes

An optional, Git-ignored attic/ holds intake and scratch files. Sources used by durable research are retained under packing/resources/.