Pith Number

pith:HAF4YSJ2

pith:2026:HAF4YSJ2QS2UPZ6W5A5NM626GV

not attested not anchored not stored refs pending

Deterministic Decomposition of Stochastic Generative Dynamics

Naoya Takeishi, Xingyu Song, Yuan Mei

The deterministic velocity field in stochastic generative processes splits into a transport component and an osmotic component fixed by the marginal score.

arxiv:2605.08794 v2 · 2026-05-09 · cs.LG · cs.AI

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\usepackage{pith}
\pithnumber{HAF4YSJ2QS2UPZ6W5A5NM626GV}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The deterministic field b_t of a stochastic generative process admits a natural transport-osmotic decomposition b_t = u_t + d_t, where u_t governs marginal probability transport and d_t captures an osmotic effect induced by diffusion and determined by the marginal score.

C2weakest assumption

That the decomposition b_t = u_t + d_t is natural, that d_t is fully and uniquely determined by the marginal score, and that recombining the components with a scalar lambda_d yields meaningful control without introducing new artifacts.

C3one line summary

Stochastic generative dynamics admit a transport-osmotic decomposition of the deterministic field, supporting Bridge Matching for interpretable and tunable generation.

Receipt and verification

First computed	2026-05-20T00:03:15.449031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

380bcc493a84b547e7d6e83ad67b5e35428274703ad7c1caba6f4dd105c0fd91

Aliases

arxiv: 2605.08794 · arxiv_version: 2605.08794v2 · doi: 10.48550/arxiv.2605.08794 · pith_short_12: HAF4YSJ2QS2U · pith_short_16: HAF4YSJ2QS2UPZ6W · pith_short_8: HAF4YSJ2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HAF4YSJ2QS2UPZ6W5A5NM626GV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 380bcc493a84b547e7d6e83ad67b5e35428274703ad7c1caba6f4dd105c0fd91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e2d44d80b511ceb910305329f4f492029596996a5f0355ce1430f3952630fd1",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-09T08:31:17Z",
    "title_canon_sha256": "fe3c88758f25a6d7600b36b0c637ddcd832b03b57ba4d6e1526cea173b7982b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08794",
    "kind": "arxiv",
    "version": 2
  }
}