Pith Number

pith:WC25V5YV

pith:2011:WC25V5YVJI6FVRVOZF6FF4VR4O

not attested not anchored not stored refs pending

Steenrod-Cech homology-cohomology theories associated with bivariant functors

Kohei Yoshida

arxiv:1112.6082 v1 · 2011-12-28 · 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{WC25V5YVJI6FVRVOZF6FF4VR4O}

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	2026-05-18T04:05:36.863023Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0b5daf7154a3c5ac6aec97c52f2b1e3bbab7a9a96a5273d1412aa7bf7552eea

Aliases

arxiv: 1112.6082 · arxiv_version: 1112.6082v1 · doi: 10.48550/arxiv.1112.6082 · pith_short_12: WC25V5YVJI6F · pith_short_16: WC25V5YVJI6FVRVO · pith_short_8: WC25V5YV

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/WC25V5YVJI6FVRVOZF6FF4VR4O \
  | 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: b0b5daf7154a3c5ac6aec97c52f2b1e3bbab7a9a96a5273d1412aa7bf7552eea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71ae4bee68f69d2ab6a803f7895e01d0175cee020c8e5d388410bf69b3c0dfa1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-12-28T08:59:40Z",
    "title_canon_sha256": "f723650277cb7f1c03edc0001fa4d98757f671bc4e44c51ed534455ff78eb7e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.6082",
    "kind": "arxiv",
    "version": 1
  }
}