Add a reversible quadratic phase stream with linear scalar work

[aliromman]

PR #1038 evaluates Machin and Taylor series at every data site. This package
replaces that phase interface with two reversible dyadic phase states.
It uses a fixed second difference, bounded three-shear rotations, and
Q=W+2 bit_length(L+1)+20 state bits. Every pass reconstructs its phase
state backward. Seed and chart coefficients clear exactly. No phase
array or checkpoint list is stored.

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

The proof gives a uniform quadratic drift bound and the same emitted
coefficient accuracy as PR #1038. The retained dirty wrappers therefore
keep their large-target error bound, exact source and borrowed-array
restoration, original precision, and two-data-tape movement bill. One
prepared phase object serves all four passes of a complete dirty word.
Its stream uses 60L+6 real products and 24L chart divisions. Exact
seed preparation and erasure add O(P) scalar operations on wider
rational operands, where P=Q+24.

Status: enabling construction. The elementary phase bit bound is
O((A+V)^2+P S^2+L T^2), where A is the original numerator width,
V is the modulus width, S=16(P+V+1)^2, and T covers stream and
data widths. A direct reversible arithmetic compiler needs
O((A+V)^2+S^2+T^2) clean scratch bits. The Python reference implements
the scalar state and exact series cleanup; it does not emit a native
bit-gate program. No new kappa is claimed.

The base is abdc6a7002abdbcd9e21bfc5e1a795784deacfdf. PR #1038 is pinned
at 99c71d385171480ecc2c43287aa4a04e1027fcd9; nine retained files have
Git-blob and SHA256 pins. No moving selected-result file is source-pinned.
PR #1054 and PR #1025 are scope references, not combined theorems. The
inherited logarithmic borrowed-array pool stays fixed. Supplier hosting,
factor production, multi-axis composition, and outer assembly stay open.

Verification:

python3 -I -O -B research/dirty-stride-fast-phases/verify.py
python3 -I -O -B research/dirty-stride-fast-phases/test_package.py

The main receipt covers 98 phase cases, 1,474 rational interval samples,
16 dirty words, three same-input work comparisons, and seven input or
lifecycle controls. It executes and reverses all 16,384 steps of the
long case. The package check rejects seven semantic faults and source
corruption, then replays the full receipt from read-only relocated files.
It returned 0 in 245.149 seconds. The parent agent also completed the
optimized main replay. These checks are finite evidence for the written
proof, not independent human review or formal multiplication verification.

Timing results are mixed. Three alternating same-input trials give
PR #1038/new median seconds of 0.042217/0.191425 at (L,W)=(32,16),
0.689942/1.286691 at (257,48), and 10.187936/9.092779 at
(2048,96). New seed erasure is included. Seed operands reach 55,767
bits in the last case. All final trials and an earlier run's medians
are disclosed. The shared-host timings do not establish a general
speedup. The result is the proved interface and its separate work bill.

NOTICE.md preserves predecessor credit and discloses substantial OpenAI
Codex assistance. New material is by Ali Romman (@aliromman) under Apache-2.0.
upstream/, selected certificates, and the research ledger are unchanged.

[Mister-Meeseeks]

100-PR batch review at 1627bf208f80e490522343590dd52f38b329e238.

This remains open after scoped triage. Next review step: Uniform dirty-stride phase/accuracy theorem depends on pending #1038 family; joint proof-interface audit required.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

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