Pith Number

pith:BTLJI6NN

pith:1999:BTLJI6NNGOEKLQBYVP2JMX3IUM

not attested not anchored not stored refs pending

Joins for (Augmented) Simplicial Sets

P.J. Ehlers, T. Porter

arxiv:math/9904039 v1 · 1999-04-09 · math.CT · 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{BTLJI6NNGOEKLQBYVP2JMX3IUM}

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.

Cited by

1 paper in Pith

Combinatorial Models for Linear Homotopy Theories

Receipt and verification

First computed	2026-07-04T14:41:06.863797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0cd69479ad3388a5c038abf4965f68a33eb1f4a2b0b9c2c579d8ea575ad9381a

Aliases

arxiv: math/9904039 · arxiv_version: math/9904039v1 · doi: 10.48550/arxiv.math/9904039 · pith_short_12: BTLJI6NNGOEK · pith_short_16: BTLJI6NNGOEKLQBY · pith_short_8: BTLJI6NN

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/BTLJI6NNGOEKLQBYVP2JMX3IUM \
  | 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: 0cd69479ad3388a5c038abf4965f68a33eb1f4a2b0b9c2c579d8ea575ad9381a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ed4585b9c4bcdf3425b40b704ddc99d720c07c496f1a0c11ef60152d7a5a805",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.CT",
    "submitted_at": "1999-04-09T11:57:29Z",
    "title_canon_sha256": "6744633ff376cefefb954e0a9f64680f96efb0a2d6b7c8d1761c15272f336da8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9904039",
    "kind": "arxiv",
    "version": 1
  }
}