Pith Number

pith:HI4VIGZF

pith:2025:HI4VIGZFDZZZIZZNDUODVWMQ2Q

not attested not anchored not stored refs pending

The extension dimension of group graded rings

Pei Luo, Zhongkui Liu

arxiv:2511.13255 v2 · 2025-11-17 · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HI4VIGZFDZZZIZZNDUODVWMQ2Q}

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	2026-06-12T01:09:16.555410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a39541b251e7394672d1d1c3ad990d403cf2e383f4477e79f9eae664e47b1a4

Aliases

arxiv: 2511.13255 · arxiv_version: 2511.13255v2 · doi: 10.48550/arxiv.2511.13255 · pith_short_12: HI4VIGZFDZZZ · pith_short_16: HI4VIGZFDZZZIZZN · pith_short_8: HI4VIGZF

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/HI4VIGZFDZZZIZZNDUODVWMQ2Q \
  | 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: 3a39541b251e7394672d1d1c3ad990d403cf2e383f4477e79f9eae664e47b1a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb488a3ea100c046d769ff6f84eef87d22a3c9b23e9522e1342ede820f9ac660",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-11-17T11:13:36Z",
    "title_canon_sha256": "1bdcd6aa57079d2e43299910b31e3392c571d7d65066170d9b449a5fd6146d71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.13255",
    "kind": "arxiv",
    "version": 2
  }
}