Pith Number

pith:METZZUMR

pith:2010:METZZUMRRFRG74MRXLSEZPGV5E

not attested not anchored not stored refs pending

Relative categories: Another model for the homotopy theory of homotopy theories

C. Barwick, D. M. Kan

arxiv:1011.1691 v2 · 2010-11-08 · 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{METZZUMRRFRG74MRXLSEZPGV5E}

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	2026-05-18T04:32:02.491040Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61279cd19189626ff191bae44cbcd5e90245f21755ab94bb3e7127c56ad5f28e

Aliases

arxiv: 1011.1691 · arxiv_version: 1011.1691v2 · doi: 10.48550/arxiv.1011.1691 · pith_short_12: METZZUMRRFRG · pith_short_16: METZZUMRRFRG74MR · pith_short_8: METZZUMR

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/METZZUMRRFRG74MRXLSEZPGV5E \
  | 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: 61279cd19189626ff191bae44cbcd5e90245f21755ab94bb3e7127c56ad5f28e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc276f5dc27d9243685a045d0d89c5657cd0141cabb8404a08d60248d7d8ca44",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2010-11-08T00:03:07Z",
    "title_canon_sha256": "f8530d7b81d0cbd004f122e516f9f57bb9c0099965827b7788a3b2f41bc7c026"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1691",
    "kind": "arxiv",
    "version": 2
  }
}