Pith Number

pith:E5GZNXWX

pith:2011:E5GZNXWX3QW36A46FODOG6Z72O

not attested not anchored not stored refs pending

A Thomason-like Quillen equivalence between quasi-categories and relative categories

C. Barwick, D. M. Kan

arxiv:1101.0772 v1 · 2011-01-04 · 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{E5GZNXWX3QW36A46FODOG6Z72O}

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	2026-05-18T04:32:02.130343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

274d96ded7dc2dbf039e2b86e37b3fd3b08c39f97de71d6323fac062bcd20d48

Aliases

arxiv: 1101.0772 · arxiv_version: 1101.0772v1 · doi: 10.48550/arxiv.1101.0772 · pith_short_12: E5GZNXWX3QW3 · pith_short_16: E5GZNXWX3QW36A46 · pith_short_8: E5GZNXWX

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/E5GZNXWX3QW36A46FODOG6Z72O \
  | 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: 274d96ded7dc2dbf039e2b86e37b3fd3b08c39f97de71d6323fac062bcd20d48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cee75fa20a491f0d303806483fb502719ea46105ece4aad6aab2e64fa25cbdf",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-01-04T17:28:39Z",
    "title_canon_sha256": "bba1ea1b548175bdacb0594edf85da937275f80cf7be129ce375eeb078b01583"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0772",
    "kind": "arxiv",
    "version": 1
  }
}