Pith Number

pith:QYPJJFWF

pith:1999:QYPJJFWF5F5WNIKBVWLULDPQP4

not attested not anchored not stored refs pending

Positivity in equivariant Schubert calculus

William Graham

arxiv:math/9908172 v1 · 1999-08-31 · math.AG · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QYPJJFWF5F5WNIKBVWLULDPQP4}

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	2026-07-04T14:41:17.649674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

861e9496c5e97b66a141ad97458df07f1785b07ec7194f2544d4f7715e83dd4e

Aliases

arxiv: math/9908172 · arxiv_version: math/9908172v1 · doi: 10.48550/arxiv.math/9908172 · pith_short_12: QYPJJFWF5F5W · pith_short_16: QYPJJFWF5F5WNIKB · pith_short_8: QYPJJFWF

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/QYPJJFWF5F5WNIKBVWLULDPQP4 \
  | 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: 861e9496c5e97b66a141ad97458df07f1785b07ec7194f2544d4f7715e83dd4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bed813d4dfeef2b3826bc9a49cb2f48f3fb468da84417fa0d4fc952850b791b",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "1999-08-31T22:12:37Z",
    "title_canon_sha256": "87a80a59ebfad69f29c6dbfc5cc06056abab1e4244fbea9634cc9c15a5bb2a3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9908172",
    "kind": "arxiv",
    "version": 1
  }
}