Pith Number

pith:F4GL7BYJ

pith:2017:F4GL7BYJTTEWOQBT76AWPXNMLU

not attested not anchored not stored refs pending

A remark on the group-completion theorem

Simon Gritschacher

arxiv:1709.02036 v1 · 2017-09-07 · 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{F4GL7BYJTTEWOQBT76AWPXNMLU}

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	2026-05-18T00:35:50.427701Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f0cbf87099cc9674033ff8167ddac5d0b620294761e30ddb80bed9fb44b3bb7

Aliases

arxiv: 1709.02036 · arxiv_version: 1709.02036v1 · doi: 10.48550/arxiv.1709.02036 · pith_short_12: F4GL7BYJTTEW · pith_short_16: F4GL7BYJTTEWOQBT · pith_short_8: F4GL7BYJ

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/F4GL7BYJTTEWOQBT76AWPXNMLU \
  | 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: 2f0cbf87099cc9674033ff8167ddac5d0b620294761e30ddb80bed9fb44b3bb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5bceada276cee83612d2b9f06f2f5296ba5e235f9e09ed2b7e6cb2426ee459d9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2017-09-07T01:10:40Z",
    "title_canon_sha256": "b274a419f22b131f7e42113d20411dbbd2032bbf2038c9c47e42ec578425aeda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.02036",
    "kind": "arxiv",
    "version": 1
  }
}