Pith Number

pith:A2QFGGNT

pith:2009:A2QFGGNTICKGX6JSMJ3UCHCCSV

not attested not anchored not stored refs pending

Middle Convolution and Harnad Duality

Daisuke Yamakawa

arxiv:0911.3863 v2 · 2009-11-19 · math.CA · 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{A2QFGGNTICKGX6JSMJ3UCHCCSV}

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	2026-05-18T04:42:12.436074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06a05319b340946bf9326277411c4295491d47cac63382af555a13a09d7cae58

Aliases

arxiv: 0911.3863 · arxiv_version: 0911.3863v2 · doi: 10.48550/arxiv.0911.3863 · pith_short_12: A2QFGGNTICKG · pith_short_16: A2QFGGNTICKGX6JS · pith_short_8: A2QFGGNT

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/A2QFGGNTICKGX6JSMJ3UCHCCSV \
  | 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: 06a05319b340946bf9326277411c4295491d47cac63382af555a13a09d7cae58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "908428715e7e12ac36619a52c15dc67c635269914d322baec5dda4b99367c942",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-11-19T18:44:29Z",
    "title_canon_sha256": "ed22ff6bc8e6da506bb6eed15e53cae1cb3af586136396933cbf10bcf42df61a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.3863",
    "kind": "arxiv",
    "version": 2
  }
}