Pith Number

pith:42Y72ICP

pith:2015:42Y72ICP5XGFRUD2BJK2OIK7MJ

not attested not anchored not stored refs pending

A higher dimensional generalization of Lichtenbaum duality in terms of the Albanese map

Wataru Kai

arxiv:1512.02026 v2 · 2015-12-07 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{42Y72ICP5XGFRUD2BJK2OIK7MJ}

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	2026-05-17T23:53:13.487039Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6b1fd204fedcc58d07a0a55a7215f62403296afcde96aa6d554139508f76e46

Aliases

arxiv: 1512.02026 · arxiv_version: 1512.02026v2 · doi: 10.48550/arxiv.1512.02026 · pith_short_12: 42Y72ICP5XGF · pith_short_16: 42Y72ICP5XGFRUD2 · pith_short_8: 42Y72ICP

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/42Y72ICP5XGFRUD2BJK2OIK7MJ \
  | 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: e6b1fd204fedcc58d07a0a55a7215f62403296afcde96aa6d554139508f76e46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02e9c8bbc6d3370d7f9b4d913f50d85af5bb38cfdcb58513e42b9961a31f3488",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-12-07T13:00:46Z",
    "title_canon_sha256": "5ed6e04e83db780ab307eeddcbb3d0a7cb9db92c3ca98e11178ec029fec967e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02026",
    "kind": "arxiv",
    "version": 2
  }
}