Pith Number

pith:KRBAJSUN

pith:2008:KRBAJSUNU7ZYTNOZ75BPHR5LV5

not attested not anchored not stored refs pending

Duality and products in algebraic (co)homology theories

Niels Kowalzig, Ulrich Kraehmer

arxiv:0812.4312 v2 · 2008-12-22 · math.QA · 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{KRBAJSUNU7ZYTNOZ75BPHR5LV5}

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	2026-05-18T01:33:57.386778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

544204ca8da7f389b5d9ff42f3c7abaf5c5d6a55b8edec22401a4f7143ebfcfa

Aliases

arxiv: 0812.4312 · arxiv_version: 0812.4312v2 · doi: 10.48550/arxiv.0812.4312 · pith_short_12: KRBAJSUNU7ZY · pith_short_16: KRBAJSUNU7ZYTNOZ · pith_short_8: KRBAJSUN

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/KRBAJSUNU7ZYTNOZ75BPHR5LV5 \
  | 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: 544204ca8da7f389b5d9ff42f3c7abaf5c5d6a55b8edec22401a4f7143ebfcfa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8174c4cdd4923d52f6bb4a4fcf02870ae5349e211ac7487d7eb5cac3114d726d",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2008-12-22T23:34:55Z",
    "title_canon_sha256": "67961f57f564df2de1f5d3cbe823706608bda3da4a9252175872ffb6e9bd313b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.4312",
    "kind": "arxiv",
    "version": 2
  }
}