Pith Number

pith:67NBLXO4

pith:2010:67NBLXO4JLRYGP5ZGLHSX6ODRZ

not attested not anchored not stored refs pending

Covering morphisms of groupoids, derived modules and a 1-dimensional Relative Hurewicz Theorem

Ronald Brown

arxiv:1012.2824 v4 · 2010-12-13 · 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{67NBLXO4JLRYGP5ZGLHSX6ODRZ}

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	2026-05-18T00:48:29.112747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7da15dddc4ae3833fb932cf2bf9c38e6ac1852aa4f61c307648747b3ee307aa

Aliases

arxiv: 1012.2824 · arxiv_version: 1012.2824v4 · doi: 10.48550/arxiv.1012.2824 · pith_short_12: 67NBLXO4JLRY · pith_short_16: 67NBLXO4JLRYGP5Z · pith_short_8: 67NBLXO4

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/67NBLXO4JLRYGP5ZGLHSX6ODRZ \
  | 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: f7da15dddc4ae3833fb932cf2bf9c38e6ac1852aa4f61c307648747b3ee307aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d69cb63834f5e31a6a854f0f8d2a4311eb6698aa0cc5e5e1a886620ca1dcde12",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2010-12-13T18:29:11Z",
    "title_canon_sha256": "10c6555773b4930b15cb1a75fc9b79df555a5ffb175b4781a60c02e6cd9c6673"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2824",
    "kind": "arxiv",
    "version": 4
  }
}