Pith Number

pith:CYXMLAJA

pith:2012:CYXMLAJA2ZPEC7HVOO7GR6AMPQ

not attested not anchored not stored refs pending

Quillen Theorems Bn for homotopy pullbacks of (infinity, k)-categories

C. Barwick, D. M. Kan

arxiv:1208.1777 v2 · 2012-08-08 · 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{CYXMLAJA2ZPEC7HVOO7GR6AMPQ}

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	2026-05-18T03:36:04.350153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

162ec58120d65e417cf573be68f80c7c2d7d75600d31a598ada38311ce0a4e5b

Aliases

arxiv: 1208.1777 · arxiv_version: 1208.1777v2 · doi: 10.48550/arxiv.1208.1777 · pith_short_12: CYXMLAJA2ZPE · pith_short_16: CYXMLAJA2ZPEC7HV · pith_short_8: CYXMLAJA

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/CYXMLAJA2ZPEC7HVOO7GR6AMPQ \
  | 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: 162ec58120d65e417cf573be68f80c7c2d7d75600d31a598ada38311ce0a4e5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "772daf9982b888d2775eedbf9538358482825299b0b65250c634aa267ec69026",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-08-08T20:25:15Z",
    "title_canon_sha256": "6427e578681450955b2f9fa06fce54c9a3bc4ec515602b6fd0b2a002fca98f4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.1777",
    "kind": "arxiv",
    "version": 2
  }
}