Pith Number

pith:QXXPH7KK

pith:2013:QXXPH7KKSSBQPYFSKG6EXD4UUQ

not attested not anchored not stored refs pending

Vector bundles from generalized pairs of cocycles

Chao You, Vladimir Manuilov

arxiv:1312.0247 v1 · 2013-12-01 · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QXXPH7KKSSBQPYFSKG6EXD4UUQ}

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	2026-05-18T03:05:46.268496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85eef3fd4a948307e0b251bc4b8f94a407622071d186ca0695d7d1ac6a1066cf

Aliases

arxiv: 1312.0247 · arxiv_version: 1312.0247v1 · doi: 10.48550/arxiv.1312.0247 · pith_short_12: QXXPH7KKSSBQ · pith_short_16: QXXPH7KKSSBQPYFS · pith_short_8: QXXPH7KK

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/QXXPH7KKSSBQPYFSKG6EXD4UUQ \
  | 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: 85eef3fd4a948307e0b251bc4b8f94a407622071d186ca0695d7d1ac6a1066cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40f9a2b6aae48bc8d7b30e77fb89928c9818d30911ce5758598cc9c3447735a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2013-12-01T16:51:44Z",
    "title_canon_sha256": "4eb1954f9e8a0c335ba2aab54aee254c098ed0181efec3a9988068a3458b56a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.0247",
    "kind": "arxiv",
    "version": 1
  }
}