Pith Number

pith:7A7PCYFK

pith:2016:7A7PCYFKGMUMPV7D76MSHUY2CC

not attested not anchored not stored refs pending

Transition formulas for involution Schubert polynomials

Brendan Pawlowski, Eric Marberg, Zachary Hamaker

arxiv:1609.09625 v4 · 2016-09-30 · math.CO · 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{7A7PCYFKGMUMPV7D76MSHUY2CC}

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	2026-05-18T00:07:12.533092Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f83ef160aa3328c7d7e3ff9923d31a10817c518bc9595b610d1b8a6924559355

Aliases

arxiv: 1609.09625 · arxiv_version: 1609.09625v4 · doi: 10.48550/arxiv.1609.09625 · pith_short_12: 7A7PCYFKGMUM · pith_short_16: 7A7PCYFKGMUMPV7D · pith_short_8: 7A7PCYFK

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/7A7PCYFKGMUMPV7D76MSHUY2CC \
  | 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: f83ef160aa3328c7d7e3ff9923d31a10817c518bc9595b610d1b8a6924559355

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0277595b8b1eb5cf03ec0838d9a5f258e13df4faad173712bcaf484a843fb791",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-30T08:07:56Z",
    "title_canon_sha256": "35c648299030efb91f4ecab019f410934fa08a68eb53a41e08b2548a9244ebcb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.09625",
    "kind": "arxiv",
    "version": 4
  }
}