Pith Number

pith:WUFUNRVL

pith:2011:WUFUNRVLLCGTB37DBWJ72YTWIC

not attested not anchored not stored refs pending

Duality with expanding maps and shrinking maps, and its applications to Gauss maps

Katsuhisa Furukawa

arxiv:1110.4841 v3 · 2011-10-21 · 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{WUFUNRVLLCGTB37DBWJ72YTWIC}

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	2026-05-18T03:00:11.661767Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b50b46c6ab588d30efe30d93fd6276408e8287d55b9d507d74a3f639b45b40c1

Aliases

arxiv: 1110.4841 · arxiv_version: 1110.4841v3 · doi: 10.48550/arxiv.1110.4841 · pith_short_12: WUFUNRVLLCGT · pith_short_16: WUFUNRVLLCGTB37D · pith_short_8: WUFUNRVL

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/WUFUNRVLLCGTB37DBWJ72YTWIC \
  | 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: b50b46c6ab588d30efe30d93fd6276408e8287d55b9d507d74a3f639b45b40c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8b42209bb4b4254d002ade7e84d920d6648b5e72fb59701b8570cacda4a8483",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-10-21T17:09:26Z",
    "title_canon_sha256": "77d3e990781f256c0267acd45965768e8e742a543c870ba75ca616839a4799d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4841",
    "kind": "arxiv",
    "version": 3
  }
}