Pith Number

pith:XPY5KLSV

pith:2026:XPY5KLSVLSZKRJ4TLLOI5D7VVQ

not attested not anchored not stored refs pending

A Riemann-Roch theorem for Frobenius quotients

Andreas Gross, Leonid Monin, Matthew Dupraz

arxiv:2607.26176 v1 · 2026-07-28 · math.AG · math.AC · math.CO · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XPY5KLSVLSZKRJ4TLLOI5D7VVQ}

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	2026-07-30T00:08:38.285929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

bbf1d52e555cb2a8a7935adc8e8ff5ac0ebd73756a493386555cc934feb37fc0

Aliases

arxiv: 2607.26176 · arxiv_version: 2607.26176v1 · doi: 10.48550/arxiv.2607.26176 · pith_short_12: XPY5KLSVLSZK · pith_short_16: XPY5KLSVLSZKRJ4T · pith_short_8: XPY5KLSV

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/XPY5KLSVLSZKRJ4TLLOI5D7VVQ \
  | 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: bbf1d52e555cb2a8a7935adc8e8ff5ac0ebd73756a493386555cc934feb37fc0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd98c2cb0e6c588bbdfbfed69c9ba50379663604eed837597e7a699c3026878f",
    "cross_cats_sorted": [
      "math.AC",
      "math.CO",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-07-28T18:31:56Z",
    "title_canon_sha256": "bd310308bb4a03b089e4672c4d09b710d1010fa9114839c025f8241d6f0fb025"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26176",
    "kind": "arxiv",
    "version": 1
  }
}