Pith Number

pith:M4JCAN32

pith:2012:M4JCAN32D52NKC467OUF6HF6IO

not attested not anchored not stored refs pending

Grothendieck groups of complexes with null-homotopies

Daniel Dugger

arxiv:1212.2143 v1 · 2012-12-10 · math.KT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M4JCAN32D52NKC467OUF6HF6IO}

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	2026-05-18T03:38:46.950087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

671220377a1f74d50b9efba85f1cbe4399f69b845c17b12ace81acd45eebf226

Aliases

arxiv: 1212.2143 · arxiv_version: 1212.2143v1 · doi: 10.48550/arxiv.1212.2143 · pith_short_12: M4JCAN32D52N · pith_short_16: M4JCAN32D52NKC46 · pith_short_8: M4JCAN32

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/M4JCAN32D52NKC467OUF6HF6IO \
  | 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: 671220377a1f74d50b9efba85f1cbe4399f69b845c17b12ace81acd45eebf226

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "618c7a24259de3c600a864efa7650e1a11164130b455a0ea5fb47085bb27b7fc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2012-12-10T17:26:25Z",
    "title_canon_sha256": "f27c41d4d08871f3628aade29c099ce229e2e8a58fb743ecf738f0243e80f45e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2143",
    "kind": "arxiv",
    "version": 1
  }
}