Pith Number

pith:4ORQ3F3N

pith:2021:4ORQ3F3NP4ETF2UOQ6LDMATJI4

not attested not anchored not stored refs pending

Polynomial log-volume growth in slow dynamics and the GK-dimensions of twisted homogeneous coordinate rings

De-Qi Zhang, Hsueh-Yung Lin, Keiji Oguiso

arxiv:2104.03423 v4 · 2021-04-07 · math.AG · math.DS · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ORQ3F3NP4ETF2UOQ6LDMATJI4}

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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.

Cited by

1 paper in Pith

An upper bound for polynomial volume growth of automorphisms of zero entropy

Receipt and verification

First computed	2026-06-11T01:09:06.102221Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3a30d976d7f0932ea8e8796360269472d89f8e13d4528cecec9e7df7e36ba29

Aliases

arxiv: 2104.03423 · arxiv_version: 2104.03423v4 · doi: 10.48550/arxiv.2104.03423 · pith_short_12: 4ORQ3F3NP4ET · pith_short_16: 4ORQ3F3NP4ETF2UO · pith_short_8: 4ORQ3F3N

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/4ORQ3F3NP4ETF2UOQ6LDMATJI4 \
  | 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: e3a30d976d7f0932ea8e8796360269472d89f8e13d4528cecec9e7df7e36ba29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc61687c442e7da7409a89cd97c7033494707b17bd5d1ec00e302ea5b0376907",
    "cross_cats_sorted": [
      "math.DS",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2021-04-07T22:44:13Z",
    "title_canon_sha256": "955dd4c158551312516a49b5406f5e0bf53972bd1bbbd0a55977870e2976ffa4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.03423",
    "kind": "arxiv",
    "version": 4
  }
}