Pith Number

pith:47VRFGYZ

pith:2012:47VRFGYZVTYCWUDWFRPEMT5AB5

not attested not anchored not stored refs pending

The Lax-Oleinik semi-group: a Hamiltonian point of view

Patrick Bernard (CEREMADE)

arxiv:1203.3569 v1 · 2012-03-15 · 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{47VRFGYZVTYCWUDWFRPEMT5AB5}

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	2026-05-18T03:59:59.669635Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7eb129b19acf02b50762c5e464fa00f42efc2cd5292f144bc4aa9390c299c16

Aliases

arxiv: 1203.3569 · arxiv_version: 1203.3569v1 · doi: 10.48550/arxiv.1203.3569 · pith_short_12: 47VRFGYZVTYC · pith_short_16: 47VRFGYZVTYCWUDW · pith_short_8: 47VRFGYZ

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/47VRFGYZVTYCWUDWFRPEMT5AB5 \
  | 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: e7eb129b19acf02b50762c5e464fa00f42efc2cd5292f144bc4aa9390c299c16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11241aabb075ac0e88df1a66ccf01f8dcb5c7ec9659869738d9db3efd2313740",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-03-15T21:18:31Z",
    "title_canon_sha256": "403c534ea73c261322a5b2a1882e02ee82f18b627e7959d7ecd12dc3ec664067"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.3569",
    "kind": "arxiv",
    "version": 1
  }
}