Pith Number

pith:I23B7NMJ

pith:2009:I23B7NMJFARRI7ZR6JGULKL5C3

not attested not anchored not stored refs pending

Branching Schubert calculus and the Belkale-Kumar product on cohomology

Edward Richmond, Nicolas Ressayre (I3M)

arxiv:0909.0865 v1 · 2009-09-04 · 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{I23B7NMJFARRI7ZR6JGULKL5C3}

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	2026-05-18T03:52:51.716190Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46b61fb5892823147f31f24d45a97d16de6b51302bd1ab042a14f310d0f727fc

Aliases

arxiv: 0909.0865 · arxiv_version: 0909.0865v1 · doi: 10.48550/arxiv.0909.0865 · pith_short_12: I23B7NMJFARR · pith_short_16: I23B7NMJFARRI7ZR · pith_short_8: I23B7NMJ

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/I23B7NMJFARRI7ZR6JGULKL5C3 \
  | 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: 46b61fb5892823147f31f24d45a97d16de6b51302bd1ab042a14f310d0f727fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "344b79aa8cf8947b3d9235144dd9e9f38ce335e2d61a9a3b9d75fca1ca5e9446",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-09-04T12:05:54Z",
    "title_canon_sha256": "c7f90c1e31d859c59002c064f08090c6670aab392edcf5b1a1bf461b80237199"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0865",
    "kind": "arxiv",
    "version": 1
  }
}