Pith Number

pith:5KXVKP4Q

pith:2007:5KXVKP4Q5FOIVDPA4TLP5XNT7G

not attested not anchored not stored refs pending

A curious example of two model categories and some associated differential graded algebras

Brooke Shipley, Daniel Dugger

arxiv:0710.3070 v1 · 2007-10-16 · 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{5KXVKP4Q5FOIVDPA4TLP5XNT7G}

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	2026-05-18T02:41:51.890812Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eaaf553f90e95c8a8de0e4d6feddb3f99fdacf483df52eb992e946b9d528de34

Aliases

arxiv: 0710.3070 · arxiv_version: 0710.3070v1 · doi: 10.48550/arxiv.0710.3070 · pith_short_12: 5KXVKP4Q5FOI · pith_short_16: 5KXVKP4Q5FOIVDPA · pith_short_8: 5KXVKP4Q

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/5KXVKP4Q5FOIVDPA4TLP5XNT7G \
  | 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: eaaf553f90e95c8a8de0e4d6feddb3f99fdacf483df52eb992e946b9d528de34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7114aa4043e48d439ecd90948b7abba2cff11f4a4d320a94ce8b70835d300d0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "2007-10-16T14:47:27Z",
    "title_canon_sha256": "bb7e93ea8c0804138ef8be8f5f1e97c7c0b5b42e49a88382650c19af0336d1f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.3070",
    "kind": "arxiv",
    "version": 1
  }
}