Pith Number

pith:3R3MKRQ7

pith:2003:3R3MKRQ7MI6RRY4G3FDV6YHNQO

not attested not anchored not stored refs pending

Algorithm for multiplying Schubert classes

Haibao Duan, Xuezhi Zhao

arxiv:math/0309158 v4 · 2003-09-09 · math.AG · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3R3MKRQ7MI6RRY4G3FDV6YHNQO}

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	2026-05-18T02:55:04.507133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc76c5461f623d18e386d9475f60ed83b54f1833e998460ac2cb5a81fdcd9762

Aliases

arxiv: math/0309158 · arxiv_version: math/0309158v4 · doi: 10.48550/arxiv.math/0309158 · pith_short_12: 3R3MKRQ7MI6R · pith_short_16: 3R3MKRQ7MI6RRY4G · pith_short_8: 3R3MKRQ7

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/3R3MKRQ7MI6RRY4G3FDV6YHNQO \
  | 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: dc76c5461f623d18e386d9475f60ed83b54f1833e998460ac2cb5a81fdcd9762

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "544c85924bbdd2b8d819b2954bbc1e82bdf2a00917958b338ad1033be3064f04",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2003-09-09T03:58:43Z",
    "title_canon_sha256": "5ea357d25fca2940306d9743dd2dae0ed6443744b2ba8ac9954c5456e51c29af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0309158",
    "kind": "arxiv",
    "version": 4
  }
}