Pith Number

pith:RTPHL3AX

pith:2025:RTPHL3AXLX2WXZKGOA6UUQTP57

not attested not anchored not stored refs pending

Billey-Postnikov posets, rationally smooth Schubert varieties, and Poincar\'e duality

Christian Gaetz, Yibo Gao

arxiv:2512.08168 v2 · 2025-12-09 · 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{RTPHL3AXLX2WXZKGOA6UUQTP57}

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	2026-06-09T02:08:35.775981Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8cde75ec175df56be546703d4a426fefe09dd10ada172ab640844308922f724b

Aliases

arxiv: 2512.08168 · arxiv_version: 2512.08168v2 · doi: 10.48550/arxiv.2512.08168 · pith_short_12: RTPHL3AXLX2W · pith_short_16: RTPHL3AXLX2WXZKG · pith_short_8: RTPHL3AX

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/RTPHL3AXLX2WXZKGOA6UUQTP57 \
  | 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: 8cde75ec175df56be546703d4a426fefe09dd10ada172ab640844308922f724b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b6a7643f80f5bb89aacc27b082411cab9e7fd93618179ee541e21098961afde",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-12-09T01:51:50Z",
    "title_canon_sha256": "82b463f7878373dec163ebdf12a3ef8cbd6a8ef9a533f986fe7c758b5d2144fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.08168",
    "kind": "arxiv",
    "version": 2
  }
}