Pith Number

pith:LXRE5Y43

pith:1998:LXRE5Y43HJKN73K7VFCTECD67S

not attested not anchored not stored refs pending

Fibrations and homotopy colimits of simplicial sheaves

Charles Rezk

arxiv:math/9811038 v2 · 1998-11-06 · 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{LXRE5Y43HJKN73K7VFCTECD67S}

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	2026-07-04T14:40:51.470373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5de24ee39b3a54dfed5fa94532087efca077fca06387fa214202943181b1cfb4

Aliases

arxiv: math/9811038 · arxiv_version: math/9811038v2 · doi: 10.48550/arxiv.math/9811038 · pith_short_12: LXRE5Y43HJKN · pith_short_16: LXRE5Y43HJKN73K7 · pith_short_8: LXRE5Y43

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/LXRE5Y43HJKN73K7VFCTECD67S \
  | 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: 5de24ee39b3a54dfed5fa94532087efca077fca06387fa214202943181b1cfb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ddabcfd226434c468ad71cbe07c11ffbe6652ea6bb21faa2cf31068045ae8735",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "1998-11-06T21:36:07Z",
    "title_canon_sha256": "65fbcaeaae02fb02c684b594b64f41612af726344e44202ee4cf3d9720ba7644"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9811038",
    "kind": "arxiv",
    "version": 2
  }
}