Pith Number

pith:I4FIENYU

pith:2026:I4FIENYU27KWRVYQH6GZMCXT4T

not attested not anchored not stored refs pending

Gradient Mean-Field Dynamics with Measure-Valued States: Well-Posedness, Chaos, and Long-Time Stability

Anderson Melchor Hernandez

arxiv:2606.24385 v1 · 2026-06-23 · math.PR · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I4FIENYU27KWRVYQH6GZMCXT4T}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-06-24T01:15:29.196608Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

470a823714d7d568d7103f8d960af3e4e506d52c9c2b3d0127a7e374eecab8a5

Aliases

arxiv: 2606.24385 · arxiv_version: 2606.24385v1 · doi: 10.48550/arxiv.2606.24385 · pith_short_12: I4FIENYU27KW · pith_short_16: I4FIENYU27KWRVYQ · pith_short_8: I4FIENYU

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/I4FIENYU27KWRVYQH6GZMCXT4T \
  | 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: 470a823714d7d568d7103f8d960af3e4e506d52c9c2b3d0127a7e374eecab8a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b1d0dd7a27b714d65d282f23f2991f1a523df41ec24df7b82987adc0ed3bae9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-23T10:18:28Z",
    "title_canon_sha256": "214a3c49af73dae2d75892b8cde1dd09c7fd4cd490a758cf22b851b0577ef352"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24385",
    "kind": "arxiv",
    "version": 1
  }
}