Independent verification: fixed-space ternary echo minima and rounded leaves

[aliromman]

This adds independent exact evidence for dirty echo schedules under a fixed scratch limit. The package certifies every state with 1–243 factors and 0–10 dirty arrays in the stated ternary tree class, rebuilds all 606 feasible literal witnesses, and tests the actual pinned PR #628 rounded leaves. A concrete witness uses 7,488 calls at 127 factors / nine arrays, versus PR #689's balanced 8,800, with every inverse and restoration call included.

Review files: Proof and scope · Evidence · Source pins and credit.

Status: independent mathematical verification and finite construction audit. No new κ.

Concurrent PR730 appeared before submission. It admits a broader mixed binary/ternary class and unequal prices. This PR credits that work and claims neither priority for unbalanced trees nor the minimum over that broader class. Its pinned optimizer was checked locally: at 27 factors / six arrays it gives 464 calls, whereas the strict ternary class here has minimum 512. The distinct evidence here is the full ternary state table, every feasible literal witness, the larger small-tree enumeration, and actual numerical rounded-leaf replay; PR #730 did not run the latter.

The admitted class uses three positive consecutive ordered children at every node with at least three factors, two leaf children at a two-factor node, unit leaf prices, and disjoint ancestor/child scratch pools. The proof gives the exact recurrence, feasibility boundary, identity, restoration contract and complete planning/execution bill. Planning is charged at O(s n^2) arithmetic operations and O(s n) scalar entries. This finite call reduction is not an all-size runtime or multiplication-exponent claim.

python3 -I -B research/dirty-echo-space-audit/verify.py

Expected: PASS_TERNARY_ECHO_SPACE_AUDIT 2673 cells; 606 literal witnesses; 11 controls.

Validation on Python 3.14.7 / macOS arm64:

• Independent direct enumeration of 715,401 feasible ordered triples agrees with the grouped optimizer at all 2,673 states. A separate enumeration covers 105,980 ordered trees through 14 factors.
• Every feasible witness is expanded: 3,019,051 leaf instructions, with exact call and scratch accounting.
• 78 free noncommutative replays and 39 nonlinear restoration/inverse tests cover selected trees through 243 factors.
• 40 actual PR #628 rounded-leaf executions at 5, 8, 17, 23 and 31 factors pass the dense exact inverse/error checks and exact dirty restoration. Larger witnesses have symbolic and resource checks, not numerical leaf replay.
• Eleven negative controls, isolated optimized-Python replay, relocation outside the repository, source-drift rejection, integer and boolean corrupt-certificate rejection, and output-overwrite rejection pass. Exact source, code and receipt hashes are retained.
• The selected-record check passed in the retained companion worktree with the same selected source tree. This branch adds only its research directory. The full repository suite, remote CI, proof-assistant formalization and independent human review are not claimed.

The factor lists are valid leaf-interface fixtures, not claimed prime-power inversion instances or measured supplier costs. All source access, three scans per leaf, preparation, inverse work and inherited precision costs remain charged. The later PR #673 integration bill and common-label, reversible-bit, physical-layout, tape, precision-recovery and analytic obligations remain open or inherited. upstream/ and the selected frontier are unchanged.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. OS-random assignment seed 71, adversarial mathematical audit track. No pinned sprint issue existed; the local claim records three candidates, the balanced-work overlap with PR #689, the one scope pivot, and the final overlap refresh through PR #734.

Credit and pins: @androolloyd's PR #673 (0e35f56cab3cae1eb0a99447135569d687c5695a) for the echo; Dillon Amburgey (@dillona)'s PR #689 (0dedef12f05f9a06faf9d4e1c8b1462c0e3bff3a) for the balanced baseline; Chafik Boukhalfa (@chafreaky)'s PR #628 (0768f97d06c623b8211e651543c66135796b62bf) for the numerical leaf and oracle; Sagar Thakrar (@thakrarsagar)'s concurrent PR #730 (d222e348179cc02a54d6d26dbd2838944f62c6e5) for the broader tree class. PR #714's distinct clean-root work and the earlier source lineage are credited in the package. Source notices remain byte-exact.

Prepared by Ali Romman (@aliromman) with substantial OpenAI Codex assistance. Apache-2.0. Finite replay is not formal verification of the full multiplication theorem.

[Mister-Meeseeks]

100-PR batch review at 302383e0c1ec71c50860362d3f394f85664c2445.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Fixed-space ternary echo schedules: exact static tree recurrence and emitted restored words; not a lower bound over all reversible algorithms.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.