Pith Number

pith:HPKPQVEZ

pith:2026:HPKPQVEZ4P6MA5HEA5AQDWTZWI

not attested not anchored not stored refs pending

The finite degree formula for normalized volumes

Zhiyu Liu

arxiv:2607.27032 v1 · 2026-07-29 · math.AG · math.AC · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HPKPQVEZ4P6MA5HEA5AQDWTZWI}

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	2026-07-30T01:23:23.916825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

3bd4f85499e3fcc074e4074101da79b22fb3486a78cca777a9a377fe676d4202

Aliases

arxiv: 2607.27032 · arxiv_version: 2607.27032v1 · doi: 10.48550/arxiv.2607.27032 · pith_short_12: HPKPQVEZ4P6M · pith_short_16: HPKPQVEZ4P6MA5HE · pith_short_8: HPKPQVEZ

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/HPKPQVEZ4P6MA5HEA5AQDWTZWI \
  | 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: 3bd4f85499e3fcc074e4074101da79b22fb3486a78cca777a9a377fe676d4202

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7573b293363c70865ceda23386bb1618002acaccde87b90dc3c171fca60f3689",
    "cross_cats_sorted": [
      "math.AC",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-07-29T15:25:56Z",
    "title_canon_sha256": "5ea32130e9d44d7beec3e4089195bafe1319cf0259f40773394617114067891c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27032",
    "kind": "arxiv",
    "version": 1
  }
}