Pith Number

pith:FT7UHJX5

pith:2015:FT7UHJX5CLWMMNF5UPACCKQL3X

not attested not anchored not stored refs pending

Mean-Field Pontryagin Maximum Principle

Francesco Rossi, Francesco Solombrino, Massimo Fornasier, Mattia Bongini

arxiv:1504.02236 v1 · 2015-04-09 · math.OC · math.AP · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FT7UHJX5CLWMMNF5UPACCKQL3X}

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	2026-05-18T02:19:15.681865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2cff43a6fd12ecc634bda3c0212a0bddcc3c458c374045041a2557fc3104cea3

Aliases

arxiv: 1504.02236 · arxiv_version: 1504.02236v1 · doi: 10.48550/arxiv.1504.02236 · pith_short_12: FT7UHJX5CLWM · pith_short_16: FT7UHJX5CLWMMNF5 · pith_short_8: FT7UHJX5

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/FT7UHJX5CLWMMNF5UPACCKQL3X \
  | 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: 2cff43a6fd12ecc634bda3c0212a0bddcc3c458c374045041a2557fc3104cea3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6837696909ec8eaf2f09f5a0bd36583d1c8f4141d6d47a2dbc130b53e6365761",
    "cross_cats_sorted": [
      "math.AP",
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-04-09T09:53:57Z",
    "title_canon_sha256": "c3c2587d882158d264aee1e289d06b1491ca91fd4d461e6fa525ae48f5a133db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.02236",
    "kind": "arxiv",
    "version": 1
  }
}