[P2][RAM] Reproduce n<=24 and profile transfer-matrix extension

[LightChainr]

Goal

Reproduce the cylindrical and helical finite-width sequences through the published frontier before attempting a larger width. Build an honest state-count, memory, and runtime model for n=25..28.

Priorities

1. Canonical compact encoding of non-crossing connectivity states.
2. Translation/reflection/topological-sector quotienting where valid.
3. Matrix-free dominant-eigenvalue iteration.
4. Deterministic sparse transition generation and hashing.
5. Checkpoint/restart and state sharding.
6. Modular or mixed-precision methods only after their error model is established.

Deliverables

• Reproduced p_c(n) values and digit agreement report.
• State counts, transition counts, peak RSS, and time per iteration for every width.
• Extrapolated resource table for widths 25–28.
• A profile showing whether computation is limited by arithmetic, hashing, memory bandwidth, or eigensolver convergence.
• Checkpoint format and transition hashes.

Acceptance

• Published widths and digits are reproduced before claiming an extension.
• Two independent paths validate state canonicalization on small widths.
• Hardware rental is justified by measured scaling, not guesswork.

Hardware

The 8-core/16-GB Debian host is suitable for implementation and sub-frontier reproduction. A high-memory CPU node—likely 256 GB or more—is more plausible for frontier work than a single consumer GPU. GPU acceleration is exploratory and low priority until matrix-free profiles identify a suitable kernel.

Tracked as T07 in experiments/tasks.yaml.

[LightChainr]

I’m claiming a bounded exact state-encoding slice on branch tools/issue-11-noncrossing-state-codec.

Scope: implement a canonical restricted-growth encoding for circular noncrossing connectivity partitions, exact rank/unrank over the enumerated state set, and an independent brute-force set-partition cross-check on small widths. Add deterministic Catalan-count, round-trip, crossing-rejection, and malformed-input tests.

Out of scope: no published-width transfer-matrix reproduction, eigenvalue calculation, transition generator, memory/runtime extrapolation, checkpoint format, or frontier-width claim. This closes only the first canonical-state primitive; issue #11 must remain open.

[LightChainr]

Bounded state-codec slice completed and squash-merged in PR #364, main commit 1f7bb0f5bd44ff6d0d404f9d08ebabff33f38185.

Exact conclusion: canonical restricted-growth strings and an independent recursive unlabelled-block enumerator produce identical circular noncrossing connectivity states through width 8. Counts are exactly 1,2,5,14,42,132,429,1430 (Catalan C_1 through C_8); every state passes exact rank/unrank round-trip, alternating crossings such as 0101 are rejected, and nested states such as 0110 are retained. Complete CI passed Python 3.9/3.11/3.13 and C++17.

Unresolved boundary: no transfer transition generator, topological-sector encoding, eigenvalue iteration, published-width reproduction, state/resource profile, checkpoint format, or width 25+ extension was attempted. Issue #11 remains open.

[LightChainr]

I’m claiming a second bounded state-algebra slice on branch tools/issue-11-planar-state-operations.

Scope: add exact detach and cyclic-adjacent join primitives on the canonical noncrossing connectivity states merged in #364; exhaustively verify through width eight that they remain canonical/noncrossing, are idempotent, and agree with independent block-set operations.

Out of scope: no transfer weights, row propagation, topological sectors, eigensolver, published-width reproduction, resource model, checkpointing, or frontier extension. This closes only deterministic planar state operations; issue #11 remains open.

[LightChainr]

Merged the claimed bounded slice via #377 (squash 2845d9c).

Exact result:

• added canonical detach-to-singleton and cyclic-adjacent join primitives;
• cross-checked restricted-growth-string operations against an independent explicit block-set implementation;
• exhaustively checked all 2,055 noncrossing states at widths 1–8: 15,521 cases per primitive (31,042 combined), with 10,814 state-changing cases for each primitive;
• every result remained canonical and noncrossing, both primitives were idempotent, and both implementations agreed exactly;
• the PR's full CI matrix passed: Python 3.9/3.11/3.13 and C++17.

Unresolved boundary: this does not implement transfer weights, row propagation, topological sectors, an eigensolver, published-width reproduction, resource estimates, checkpointing, or wider-frontier scaling. Those are still required for the parent deliverable, so #11 remains open.

[LightChainr]

Claiming a bounded deterministic transition-table slice on branch tools/issue-11-planar-transition-table.

Scope: generate the complete width-1..8 table of canonical detach and cyclic-adjacent join transitions from the already merged state codec/operations, serialize it canonically, freeze per-width state/case/change/unique-edge counts and SHA-256 hashes, and independently recompute every target from block-set operations.

Out of scope: transfer weights, row propagation, topological sectors, eigensolver work, published-width reproduction, memory/runtime extrapolation, checkpointing, or frontier extension. Latest main, all open PRs, and remote branches contain only the completed codec/operation branches and no transition-table work. The parent issue will remain open.

[LightChainr]

Bounded deterministic transition-table slice completed in PR #392, squash-merged as 0e1c6c11a0d775046010ab8e1c0430fea5ade885 after complete CI passed (C++17 and Python 3.9/3.11/3.13; run 33308871016).

Exact result

• Generated the complete canonical detach/join transition record stream for widths 1–8: 2,055 states, 15,521 point-cases per operation, and 31,042 total JSONL records.
• Every target state was independently recomputed by explicit block-set operations and mapped back to a canonical noncrossing-state rank; mismatch and out-of-space counts are zero.
• Froze per-width state/case/change counts, unique source-target edge counts, and row unique-target degree histograms.
• Canonical serialization order is width, source rank, boundary point, then operation; compact sorted-key JSONL has complete SHA-256 c18df595b0ff3d34a6d761b024f69fccc021e9bbf6bc6e5cc390b43ad48c462f, with separate hashes for every width.
• The complete local suite passed 856 tests (1 skipped).

Still unresolved

These are unweighted local state-algebra transitions, not a row transfer matrix. Transfer weights, deterministic row propagation, topological-sector encoding, eigenvalue iteration, published n<=24 reproduction, resource profiles, checkpoint/restart, and widths 25+ remain undone. Keeping #11 open.

[LightChainr]

Parked for the 2026-08-31 weekly decision: this remains a useful support/long-horizon line, but it is not part of the current #154/#334 validation execution. Please do not prepend new handoff blocks; resume only after docs/STATUS.md explicitly reprioritizes it (cleanup PR #528).