Pith Number

pith:B4ACM2WX

pith:2010:B4ACM2WX2NTVKG45TY5MAD26XI

not attested not anchored not stored refs pending

Frobenius pull backs of vector bundles in higher dimensions

V. Trivedi

arxiv:1011.1971 v2 · 2010-11-09 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B4ACM2WX2NTVKG45TY5MAD26XI}

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	2026-05-18T04:33:04.046346Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f00266ad7d367551b9d9e3ac00f5eba2896a7496bd97bad0dd20e3d7a62c4bd

Aliases

arxiv: 1011.1971 · arxiv_version: 1011.1971v2 · doi: 10.48550/arxiv.1011.1971 · pith_short_12: B4ACM2WX2NTV · pith_short_16: B4ACM2WX2NTVKG45 · pith_short_8: B4ACM2WX

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/B4ACM2WX2NTVKG45TY5MAD26XI \
  | 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: 0f00266ad7d367551b9d9e3ac00f5eba2896a7496bd97bad0dd20e3d7a62c4bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "640fe1141f34a622d34b040ec5adb0b54da254719ec132a2ee174633f5928635",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-11-09T04:56:00Z",
    "title_canon_sha256": "01323e1bb50b0e5725f5b230cd6cb7733f3696fcef08b60c1d68bf7997cd402d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1971",
    "kind": "arxiv",
    "version": 2
  }
}