Pith Number

pith:TW4QLXL6

pith:2012:TW4QLXL6K4HZOMQYMWW7OVBJCK

not attested not anchored not stored refs pending

Sheaf theory and Paschke duality

John Roe, Paul Siegel

arxiv:1210.6420 v1 · 2012-10-24 · 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{TW4QLXL6K4HZOMQYMWW7OVBJCK}

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	2026-05-18T03:42:24.890678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9db905dd7e570f97321865adf75429128687a0f37197d5727994ddea0c2781a7

Aliases

arxiv: 1210.6420 · arxiv_version: 1210.6420v1 · doi: 10.48550/arxiv.1210.6420 · pith_short_12: TW4QLXL6K4HZ · pith_short_16: TW4QLXL6K4HZOMQY · pith_short_8: TW4QLXL6

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/TW4QLXL6K4HZOMQYMWW7OVBJCK \
  | 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: 9db905dd7e570f97321865adf75429128687a0f37197d5727994ddea0c2781a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a28018aa99b47cb8161a6fbab8b172b66cabedd73bde85b2c2d22209263b4ca7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2012-10-24T01:49:42Z",
    "title_canon_sha256": "c24e16d3bb381cadcb36c51292cbb1f94b7656748b9c975c194d48e9cdb0ad25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6420",
    "kind": "arxiv",
    "version": 1
  }
}