Pith Number

pith:HKOPYCX7

pith:2026:HKOPYCX7CO2AAYTTNQA22FA2JW

not attested not anchored not stored refs pending

Complex normalizing flows can almost be information K\"ahler-Ricci flows

Andrew Gracyk

Complex normalizing flows recover Kähler-Ricci flow equations through their log-determinant terms.

arxiv:2604.17954 v3 · 2026-04-20 · math.DG · cs.LG

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\usepackage{pith}
\pithnumber{HKOPYCX7CO2AAYTTNQA22FA2JW}

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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 log determinant used in the complex normalizing flow matches a Ricci curvature term under differentiation and conditions, recovering a Kähler-Ricci flow variation up to a time derivative and expectation, or an average-valued Kähler-Einstein flow.

C2weakest assumption

The assumption that the log density under the normalizing flow is kindred to a spatial Fisher information metric under an augmented Jacobian and a Bayesian perspective to the parameter, allowing the continuum limit to recover the geometric flow.

C3one line summary

Complex normalizing flows nearly correspond to information Kähler-Ricci flows because the log-determinant term matches Ricci curvature under differentiation, recovering a Kähler-Ricci variation in the continuum limit.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-23T03:13:57.283411Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a9cfc0aff13b40062736c01ad141a4db71fdb2be629f619b30c0c75f9ab7814

Aliases

arxiv: 2604.17954 · arxiv_version: 2604.17954v3 · doi: 10.48550/arxiv.2604.17954 · pith_short_12: HKOPYCX7CO2A · pith_short_16: HKOPYCX7CO2AAYTT · pith_short_8: HKOPYCX7

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/HKOPYCX7CO2AAYTTNQA22FA2JW \
  | 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: 3a9cfc0aff13b40062736c01ad141a4db71fdb2be629f619b30c0c75f9ab7814

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb2378344bfe74ebad35856c029edf9c7a6a25e0ac4a8ab0d7e7a9fc4fa8d770",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-04-20T08:36:35Z",
    "title_canon_sha256": "af6748d5034e8c9d556b05963cdd041daa038cdffc9295e9a853832ff8f2d834"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.17954",
    "kind": "arxiv",
    "version": 3
  }
}