Pith Number

pith:5WC5NBKC

pith:2026:5WC5NBKCCD66TVMEBJSMZSQAJJ

not attested not anchored not stored refs pending

Analytic Bridge Diffusions for Controlled Path Generation

Michael Chertkov

Linear-quadratic-Gaussian control with Gaussian-mixture boundaries supplies closed-form scores, marginals, and protocols for bridge diffusions.

arxiv:2605.02961 v2 · 2026-05-03 · cs.LG · cond-mat.stat-mech · cs.AI · cs.SY · eess.SY · math.OC

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\pithnumber{5WC5NBKCCD66TVMEBJSMZSQAJJ}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

In LQ-GM-PID the score, intermediate marginals, and protocol gradients are available in closed form without inner stochastic simulation loops and without neural networks in the optimization loop.

C2weakest assumption

The assumption that linear dynamics, Gaussian noise, quadratic costs, and Gaussian-mixture initial/terminal laws are together sufficient to keep the Riccati-based solution closed-form when the terminal target is a prescribed density rather than a point.

C3one line summary

LQ-GM-PID recasts LQG control as a path-integral diffusion problem with Gaussian-mixture terminals to deliver closed-form bridge diffusion quantities for controlled path generation.

Formal links

3 machine-checked theorem links

Cited by

1 paper in Pith

PRISM: Principled Reference Identification for Schrodinger Bridge Model

Receipt and verification

First computed	2026-08-13T00:21:22.738784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed85d6854210fde9d5840a64ccca004a652adccafbaf8e38d043ed6bce9ce32e

Aliases

arxiv: 2605.02961 · arxiv_version: 2605.02961v2 · doi: 10.48550/arxiv.2605.02961 · pith_short_12: 5WC5NBKCCD66 · pith_short_16: 5WC5NBKCCD66TVME · pith_short_8: 5WC5NBKC

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/5WC5NBKCCD66TVMEBJSMZSQAJJ \
  | 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: ed85d6854210fde9d5840a64ccca004a652adccafbaf8e38d043ed6bce9ce32e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c2d71ca8a3590411b5500d826071e7a4a1f85a515c54f9191d958edd36d1d64",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "cs.AI",
      "cs.SY",
      "eess.SY",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-03T05:36:52Z",
    "title_canon_sha256": "a2ed6d962a5898c1cd9afbdc381148d95c3d42128a87c9c9d5ae2ffc7c441436"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02961",
    "kind": "arxiv",
    "version": 2
  }
}