Pith Number

pith:OZJ7GATD

pith:2014:OZJ7GATDOHC4JZUXBM2GGBRVMD

not attested not anchored not stored refs pending

Linear duals of graded bundles and higher analogues of (Lie) algebroids

Andrew James Bruce, Janusz Grabowski, Katarzyna Grabowska

arxiv:1409.0439 v2 · 2014-09-01 · math-ph · math.DG · math.MP · math.QA · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OZJ7GATDOHC4JZUXBM2GGBRVMD}

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	2026-05-18T01:17:01.251542Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7653f3026371c5c4e6970b3463063560e32ac68a63d29d43c8d648ca0c2a8984

Aliases

arxiv: 1409.0439 · arxiv_version: 1409.0439v2 · doi: 10.48550/arxiv.1409.0439 · pith_short_12: OZJ7GATDOHC4 · pith_short_16: OZJ7GATDOHC4JZUX · pith_short_8: OZJ7GATD

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/OZJ7GATDOHC4JZUXBM2GGBRVMD \
  | 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: 7653f3026371c5c4e6970b3463063560e32ac68a63d29d43c8d648ca0c2a8984

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c3bc9cb74482e2ea321332bd9bf050bc50e4374ea5b445190adcf8176706afd",
    "cross_cats_sorted": [
      "math.DG",
      "math.MP",
      "math.QA",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2014-09-01T14:48:04Z",
    "title_canon_sha256": "a06580e4eb3dadbff8013022ecb3c967b430c9ae6a1f83935c39f162e582cda6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.0439",
    "kind": "arxiv",
    "version": 2
  }
}