Pith Number

pith:N6J2YTMP

pith:2001:N6J2YTMPLWYF5ZQMMMLQUY5UQJ

not attested not anchored not stored refs pending

Combinatorial Tangent Space and Rational Smoothness of Schubert Varieties

St\'ephane Gaussent

arxiv:math/0103022 v1 · 2001-03-05 · 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{N6J2YTMPLWYF5ZQMMMLQUY5UQJ}

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	2026-05-18T01:05:37.875523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f93ac4d8f5db05ee60c63170a63b482761975c67b1a6b6b025c65905c4f8cc0

Aliases

arxiv: math/0103022 · arxiv_version: math/0103022v1 · doi: 10.48550/arxiv.math/0103022 · pith_short_12: N6J2YTMPLWYF · pith_short_16: N6J2YTMPLWYF5ZQM · pith_short_8: N6J2YTMP

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/N6J2YTMPLWYF5ZQMMMLQUY5UQJ \
  | 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: 6f93ac4d8f5db05ee60c63170a63b482761975c67b1a6b6b025c65905c4f8cc0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dd41b33f615d6783deec195494f9f6dac5dd7dcd16fb32011fdbcbd388e86ba",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2001-03-05T09:09:39Z",
    "title_canon_sha256": "b6db2f1be3b12104394392961bfd97eb0db3f64f20b7faef446caed7421d2fab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0103022",
    "kind": "arxiv",
    "version": 1
  }
}