Pith Number

pith:PYD7Z4BN

pith:2018:PYD7Z4BNHX7HW3PQYE3EDUCIEG

not attested not anchored not stored refs pending

Pontryagin Maximum Principle and Stokes Theorem

Andrea Spiro, Franco Cardin

arxiv:1812.07875 v2 · 2018-12-19 · math-ph · math.DG · math.MP · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PYD7Z4BNHX7HW3PQYE3EDUCIEG}

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	2026-05-17T23:42:25.550067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e07fcf02d3dfe7b6df0c13641d04821990dabdb4eeefac1b9b880a1e9261fe8

Aliases

arxiv: 1812.07875 · arxiv_version: 1812.07875v2 · doi: 10.48550/arxiv.1812.07875 · pith_short_12: PYD7Z4BNHX7H · pith_short_16: PYD7Z4BNHX7HW3PQ · pith_short_8: PYD7Z4BN

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/PYD7Z4BNHX7HW3PQYE3EDUCIEG \
  | 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: 7e07fcf02d3dfe7b6df0c13641d04821990dabdb4eeefac1b9b880a1e9261fe8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76e41a9767643bc52df2afeab26df46cc3c58f4a0ceea5d66c5c6cc508566c3f",
    "cross_cats_sorted": [
      "math.DG",
      "math.MP",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2018-12-19T11:01:07Z",
    "title_canon_sha256": "f44d694a9576e5fa67f54f63ff91984cd4bc3e46e637bbd4edd8a75a23513b58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.07875",
    "kind": "arxiv",
    "version": 2
  }
}