Pith Number

pith:SH4WCGCP

pith:2007:SH4WCGCPWNRWSPGMM2ZDW2I4D6

not attested not anchored not stored refs pending

Variational calculus with constraints on general algebroids

Janusz Grabowski, Katarzyna Grabowska

arxiv:0712.2766 v2 · 2007-12-17 · math-ph · math.DG · 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{SH4WCGCPWNRWSPGMM2ZDW2I4D6}

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	2026-05-18T04:08:04.303860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91f961184fb363693ccc66b23b691c1fad43baaf460a0fb61193ac82d09b339d

Aliases

arxiv: 0712.2766 · arxiv_version: 0712.2766v2 · doi: 10.48550/arxiv.0712.2766 · pith_short_12: SH4WCGCPWNRW · pith_short_16: SH4WCGCPWNRWSPGM · pith_short_8: SH4WCGCP

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/SH4WCGCPWNRWSPGMM2ZDW2I4D6 \
  | 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: 91f961184fb363693ccc66b23b691c1fad43baaf460a0fb61193ac82d09b339d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2309199773436e6558cda85dd9ba89316cf6a1ac6c95eab721dcdb659ca6ffe3",
    "cross_cats_sorted": [
      "math.DG",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2007-12-17T16:38:16Z",
    "title_canon_sha256": "ae38865e8d759969ffcddbe81b1fdb4de167782a06e137a45bc7312699bd9211"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.2766",
    "kind": "arxiv",
    "version": 2
  }
}