Prime Gap Generative Engine v1.0

Prime Gap Generative Engine v1.0

Prime Gap Generative Engine v1.0 is the frozen reference release for the
hierarchical reduced gap-type engine.

This release packages the first deterministic engine family in the repository
that closes the local reduced prime-gap type surface to pooled-window
concentration L1 0.0116 while also exposing a measured long-horizon reset
frontier.

Headline Freeze Metrics

• local fidelity profile:
  hybrid_lag2_mod8_reset_nontriad_scheduler
  with pooled-window concentration L1 0.0116
• balanced frontier profile:
  event-lock L = 3
  with pooled-window concentration L1 0.0150
  and full-walk three-step concentration 0.5564
• long-horizon study profile:
  event-lock L = 6
  with full-walk three-step concentration 0.6278

Named Engine Objects

• persistent 14-state core grammar
• Semiprime Wheel Attractor:
  o2_odd_semiprime|d<=4,
  o4_odd_semiprime|d<=4,
  o6_odd_semiprime|d<=4
• lag-2 scheduler plus periodic phase
• higher-divisor-triggered long-horizon reset controller

Release Artifacts

Frozen synthesis

• ../../output/gwr_dni_gap_type_engine_v1_summary.json
• 

Engine code and tests

• ../../benchmarks/python/predictor/gwr_dni_gap_type_engine_synthesis.py
• ../../tests/python/predictor/test_gwr_dni_gap_type_engine_synthesis.py

Freeze note and rulebook

• ../../gwr/findings/gap_type_engine_v1_freeze.md
• ../../gwr/findings/gap_type_engine_v1_rulebook.md

Submission draft

• ../../docs/research/predictor/prime_gap_hierarchical_engine_paper_draft.md

Synthetic example

• ../../output/gwr_dni_gap_type_generative_probe_synthetic.csv

The synthetic example contains 10,000 committed rows on the persistent core
surface. The first row and the last row are both
o4_odd_semiprime|d<=4, which makes the attractor visible immediately even in
the bare CSV.

Validation

The release state is backed by the predictor slice:

pytest -q \
  tests/python/predictor/test_gwr_dni_gap_type_sequence_probe.py \
  tests/python/predictor/test_gwr_dni_gap_type_generative_probe.py \
  tests/python/predictor/test_gwr_dni_gap_type_engine_decode.py \
  tests/python/predictor/test_gwr_dni_gap_type_scheduler_probe.py \
  tests/python/predictor/test_gwr_dni_gap_type_hybrid_scheduler_probe.py \
  tests/python/predictor/test_gwr_dni_gap_type_long_horizon_controller_probe.py \
  tests/python/predictor/test_gwr_dni_gap_type_engine_synthesis.py

Scope

This release is a claim about reduced prime-gap types, not yet a theorem about
the full raw gap-size sequence.

The current supported statement is:

On the persistent reduced gap-type surface, prime-gap types are generated by a
hierarchical finite-state engine with a 14-state core grammar, a scheduler
layer, and a higher-divisor-triggered long-horizon controller.

The current frontier remains explicit:

No single tested deterministic controller yet achieves both pooled-window
concentration L1 below 0.015 and full-walk three-step concentration above
0.62.