Add VF-1 residue-state experimental branch

[MatrixFreeSama]

Adds a conjectural verification-free residue-state representation without changing the exact main-path claim.

Key changes:

• adds source/vf_residue_state.c/.h with an explicit-stack finite-width survivor transport over residues r_j = p mod q_j;
• removes the large integer from the inner fixed-K divisibility recursion after residue initialization;
• keeps finite-width outputs explicitly PROVISIONAL / UNVERIFIED;
• adds the formal VF-1 conjecture and separates bit width L, dimension width K, recursion depth D_rec, and adaptive correction rounds R(p,K);
• adds a reproducible GMP cloud benchmark under experiments/, isolated from the Windows build;
• adds a second diagnostic K/R-collapse experiment based on the exact finite-K identity P_K = product(q_j), z = p mod P_K, J_K(z) = min{d>=1:gcd(z+d,P_K)=1};
• documents why this merges K and R algebraically but does not yet provide a valid causal-depth-1 generator: the reference evaluator still exposes offset search, a full wheel would become a forbidden/explosive lookup table, and explicit P_K still carries K-dependent information;
• compiles the new Windows-compatible residue module in the branch build.

Cloud benchmark highlights:

• fixed K=256, near 10^100: residue inner call ~1.86 us vs full-big-int ~5.90 us;
• fixed K=256, near 10^1000000: residue inner call ~3.31 us vs full-big-int ~36.4 ms;
• K/R primorial diagnostic at 10^100+267 agrees exactly with the finite-K residue vector for all tested widths: K=256 -> gap 4, K=2,048 -> 4, K=88,232 -> 6, K=175,692 -> 22;
• the independent exact successor gap for that input is 682, so the K/R algebraic collapse does not solve the missing dimension-coverage problem.

No claim is made that VF-1 is proved, that finite K returns the exact next prime, that the diagnostic prime fixture is part of generation, or that causal depth 1 has been established.

[MatrixFreeSama]

Added the event-staircase diagnostic and documentation.

For p = 10^100 + 267, the finite-width gap is a monotone staircase rather than a level-by-level drift:

• K=1, q=2: g=2
• K=2, q=3: g=4
• K=88,231, q=1,134,709: g=4 -> 6
• K=175,692, q=2,391,019: g=6 -> 22
• no further collision was found through q <= 3,000,000; p+22 is still composite in an independent post-check.

A diagnostic block-GCD locator skipped long empty plateaus. With block size 512 over the 216,816 primes <= 3,000,000, collision location used 422 block GCD tests plus 1,775 local prime tests and reproduced the same three events. The event-run portion was about 3.2 ms on the cloud CPU after the conventional diagnostic fixture was built.

Important boundary: this is not admitted as the final VF-1 generator. The block products encode a conventional prime fixture and their GCDs are effectively batched factor-location information. The useful result is structural: K and correction activity can be represented as sparse collision events, but predicting the next event without hidden least-prime-factor information remains the unresolved collapse step.

Files:

• experiments/vf1_event_staircase_gmp.c
• docs/VF1_EVENT_STAIRCASE_2026-08-25.md

[MatrixFreeSama]

Event-jump collapse attempt added.

New files:

• experiments/vf1_event_tree_gmp.c
• docs/VF1_EVENT_TREE_2026-08-25.md

Finite diagnostic at the 10^100+267 target builds a balanced product tree over the 216,816 prime dimensions <= 3,000,000. Given the tree, the two known collision events are located with 39 and 36 GCD-node probes rather than a linear K scan, and the g=22 state is rejected as collision-free through the fixture with 8 probes.

A useful exact identity is now documented: gcd(c,B_I)=gcd(c,B_I mod c). Thus an aggregate collision certificate can stay bounded by the candidate bit width even when the explicit block product would be enormous. This removes primorial payload size as a necessary representation cost, but not the cost/information of generating the dimension leaves.

The next admissible target is an implicit block transfer operator B_I(c,g)->g' that composes dimension intervals without enumerating their leaves and without exposing factor location. This is an intermediate O(log K) causal-depth route, not a claim of VF-1 proof.

[MatrixFreeSama]

Added a bounded offset-mask monoid diagnostic as the next K/R/E-collapse step. For finite K and local horizon W, each dimension contributes a periodic forbidden-offset mask, block composition is exact bitwise OR, the root payload is W bits independent of K, and finite-K correction rounds collapse to one first-zero query. At p=10^100+267 the mask reproduces 4, 4, 6, 22 at the previously observed widths. With 216,816 active dimensions, W=4096 and 512-dimension blocks, the 512-byte root was reduced in about 3.2-3.6 us after leaf construction; independently rebuilt block/flat masks agree, and the chain translation identity F^(p+g)(d)=F^p(d+g) had zero mismatches on the preserved prefix. This remains diagnostic because it still enumerates dimension leaves and materializes a bounded offset window. The remaining target is a symbolic associative summary Sigma_I that preserves the aggregate exclusion effect without O(K) leaf construction or O(W) candidate-window materialization.

[MatrixFreeSama]

Added the next symbolic-collapse diagnostic. Two concrete results:

1. Generic exact OR-monoid compression of a W-offset forbidden mask has a worst-case W-bit lower bound if it must support arbitrary future unions and exact first-zero recovery. So the existing W-bit mask is already information-theoretically optimal for the unrestricted mask problem; any sub-W VF-1 state must exploit arithmetic structure.

2. Added experiments/vf1_factorial_certificate_gmp.c, which replaces the explicit prime basis up to a value bound B by the exact bounded payload Sigma_B(c)=B! mod c, with collision predicate gcd(c,Sigma_B(c))>1. No prime table or explicit primorial is required. The modular product tree has O(log B) algebraic combination depth with constant-size leaves, while total work remains B-dependent.

At p=10^100+267 the diagnostic detects the known staircase collisions at B=1,134,709 for gap 4 and B=2,391,019 for gap 6. At B=3,000,000 it reports no collision for gap 22, consistent with the prior event-tree scan. This is still diagnostic only and not a VF-1 proof or admissible final generator.