Pith Number

pith:F4QTSTJ4

pith:2003:F4QTSTJ4KEGACHRIKBF46THJMA

not attested not anchored not stored refs pending

A Schubert calculus recurrence from the noncomplex W-action on G/B

Allen Knutson

arxiv:math/0306304 v1 · 2003-06-20 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F4QTSTJ4KEGACHRIKBF46THJMA}

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.

Cited by

1 paper in Pith

Signed puzzles for Schubert coefficients

Receipt and verification

First computed	2026-07-04T14:37:32.434784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f21394d3c510c011e28504bcf4ce96029f680f098f4ebbcc9ceefa3c93de980

Aliases

arxiv: math/0306304 · arxiv_version: math/0306304v1 · doi: 10.48550/arxiv.math/0306304 · pith_short_12: F4QTSTJ4KEGA · pith_short_16: F4QTSTJ4KEGACHRI · pith_short_8: F4QTSTJ4

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/F4QTSTJ4KEGACHRIKBF46THJMA \
  | 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: 2f21394d3c510c011e28504bcf4ce96029f680f098f4ebbcc9ceefa3c93de980

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0dbe487302491527ba3326ce0fed63391bc2d6e2afd17f4848ad4dea1405e95",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2003-06-20T00:19:09Z",
    "title_canon_sha256": "52a6115992af5f0e089c77b9170a0ce217e715618c4231df1d81e127b90bde61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0306304",
    "kind": "arxiv",
    "version": 1
  }
}