Pith Number

pith:UWAYCORW

pith:2025:UWAYCORWCN4IINRUMLATPCVWZ4

not attested not anchored not stored refs pending

Hybrid pipe dreams for the lower-upper scheme

Allen Knutson, Paul Zinn-Justin

arxiv:2509.01857 v1 · 2025-09-02 · 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{UWAYCORWCN4IINRUMLATPCVWZ4}

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	2026-07-05T12:03:10.035450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a581813a36137884363462c1378ab6cf0de8c3785ce04358e3ad21440c5c57ab

Aliases

arxiv: 2509.01857 · arxiv_version: 2509.01857v1 · doi: 10.48550/arxiv.2509.01857 · pith_short_12: UWAYCORWCN4I · pith_short_16: UWAYCORWCN4IINRU · pith_short_8: UWAYCORW

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/UWAYCORWCN4IINRUMLATPCVWZ4 \
  | 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: a581813a36137884363462c1378ab6cf0de8c3785ce04358e3ad21440c5c57ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e41c98aaeabd051497b9a1c19530da93294826a165a011ea42925aa9c153ec99",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-09-02T00:52:17Z",
    "title_canon_sha256": "7f43de7d041bcaa48f6426cd41e92c61f348eeaa485ac7af269ebede3fd8cb83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.01857",
    "kind": "arxiv",
    "version": 1
  }
}