Pith Number

pith:7Q6J72ZK

pith:2002:7Q6J72ZKNXWGZPV74SI5G7S65A

not attested not anchored not stored refs pending

Equivalences of monoidal model categories

Brooke Shipley, Stefan Schwede

arxiv:math/0209342 v2 · 2002-09-25 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7Q6J72ZKNXWGZPV74SI5G7S65A}

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	2026-05-18T02:41:32.859027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc3c9feb2a6dec6cbebfe491d37e5ee8159c7219edb1b76b46f34e42a85edee8

Aliases

arxiv: math/0209342 · arxiv_version: math/0209342v2 · doi: 10.48550/arxiv.math/0209342 · pith_short_12: 7Q6J72ZKNXWG · pith_short_16: 7Q6J72ZKNXWGZPV7 · pith_short_8: 7Q6J72ZK

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/7Q6J72ZKNXWGZPV74SI5G7S65A \
  | 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: fc3c9feb2a6dec6cbebfe491d37e5ee8159c7219edb1b76b46f34e42a85edee8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94c152d43aabca3532f3093b87365d42e97d62066c2e8770df46aebcc9ffd827",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "2002-09-25T16:06:24Z",
    "title_canon_sha256": "50b2569a73a8c9e5b44a68c75fe85a2c276760b830dd7113e260f281dc7448ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0209342",
    "kind": "arxiv",
    "version": 2
  }
}