Pith Number

pith:PT45DQEL

pith:2002:PT45DQELVEKRYNM33XONX5SWUX

not attested not anchored not stored refs pending

Smoothness of Schubert varieties via patterns in root systems

Alexander Postnikov, Sara Billey

arxiv:math/0205179 v2 · 2002-05-16 · math.CO · 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{PT45DQELVEKRYNM33XONX5SWUX}

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	2026-07-04T14:36:12.616457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cf9d1c08ba9151c359bdddcdbf656a5fd8b07e0edfb26fd7c359ce8d76b43c8

Aliases

arxiv: math/0205179 · arxiv_version: math/0205179v2 · doi: 10.48550/arxiv.math/0205179 · pith_short_12: PT45DQELVEKR · pith_short_16: PT45DQELVEKRYNM3 · pith_short_8: PT45DQEL

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/PT45DQELVEKRYNM33XONX5SWUX \
  | 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: 7cf9d1c08ba9151c359bdddcdbf656a5fd8b07e0edfb26fd7c359ce8d76b43c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d695b9d9203d8ee4e47a3118820bcba200d373b98455369e14ddb58118a01e7",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2002-05-16T02:22:37Z",
    "title_canon_sha256": "48e14170b238aa6a5d1d98b61f6471b51cefaa4d71e8a21383cdac5e57fcd2e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0205179",
    "kind": "arxiv",
    "version": 2
  }
}