Pith Number

pith:4PQUUWLZ

pith:2015:4PQUUWLZB7HGPMA4EH62KTUTX7

not attested not anchored not stored refs pending

Bounds on the degrees of birational maps with arithmetically Cohen-Macaulay graphs

Aron Simis, S. Hamid Hassanzadeh

arxiv:1504.07960 v5 · 2015-04-29 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4PQUUWLZB7HGPMA4EH62KTUTX7}

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	2026-05-18T00:52:34.575805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3e14a59790fce67b01c21fda54e93bffbdaab61abf7ba776df9bdfd977e1861

Aliases

arxiv: 1504.07960 · arxiv_version: 1504.07960v5 · doi: 10.48550/arxiv.1504.07960 · pith_short_12: 4PQUUWLZB7HG · pith_short_16: 4PQUUWLZB7HGPMA4 · pith_short_8: 4PQUUWLZ

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/4PQUUWLZB7HGPMA4EH62KTUTX7 \
  | 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: e3e14a59790fce67b01c21fda54e93bffbdaab61abf7ba776df9bdfd977e1861

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b2741fb9e6c9b66a851e1508193eb15c94aa39c8842a88b15222941049c39f4",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-04-29T18:49:45Z",
    "title_canon_sha256": "d9e0c62857d6a15817a5c0948b553186c37b1c3a895c025dc535de68b312ecd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.07960",
    "kind": "arxiv",
    "version": 5
  }
}