Pith Number

pith:VLN35CAZ

pith:2011:VLN35CAZ6X2IDPOPAYTTUXBBHO

not attested not anchored not stored refs pending

A Quillen theorem Bn for homotopy pullbacks

C. Barwick, D. M. Kan

arxiv:1101.4879 v1 · 2011-01-25 · math.AT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VLN35CAZ6X2IDPOPAYTTUXBBHO}

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	2026-05-18T04:30:58.831621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aadbbe8819f5f481bdcf06273a5c213b8c25a823a480a7b8fe6f0f3bad21a072

Aliases

arxiv: 1101.4879 · arxiv_version: 1101.4879v1 · doi: 10.48550/arxiv.1101.4879 · pith_short_12: VLN35CAZ6X2I · pith_short_16: VLN35CAZ6X2IDPOP · pith_short_8: VLN35CAZ

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/VLN35CAZ6X2IDPOPAYTTUXBBHO \
  | 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: aadbbe8819f5f481bdcf06273a5c213b8c25a823a480a7b8fe6f0f3bad21a072

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2df0dacb72256bbe79d1342732d451333d37131dfd5dd28e68d6fdee9148a30c",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-01-25T17:32:31Z",
    "title_canon_sha256": "4c05dc4bb062ee25d427800e44ef78b94042c4d095ff1e0bf7c1de6a0ae1efe6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.4879",
    "kind": "arxiv",
    "version": 1
  }
}