Pith Number

pith:AGTONAVV

pith:2016:AGTONAVVGSTEYECC6DUHYVWZFF

not attested not anchored not stored refs pending

On the additive and multiplicative structures of the exceptional units in finite commutative rings

Min Sha, Su Hu

arxiv:1612.04539 v4 · 2016-12-14 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AGTONAVVGSTEYECC6DUHYVWZFF}

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	2026-05-17T23:57:03.439410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01a6e682b534a64c1042f0e87c56d9296000ae1e56c9062b7ae4aaf9594e94d0

Aliases

arxiv: 1612.04539 · arxiv_version: 1612.04539v4 · doi: 10.48550/arxiv.1612.04539 · pith_short_12: AGTONAVVGSTE · pith_short_16: AGTONAVVGSTEYECC · pith_short_8: AGTONAVV

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/AGTONAVVGSTEYECC6DUHYVWZFF \
  | 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: 01a6e682b534a64c1042f0e87c56d9296000ae1e56c9062b7ae4aaf9594e94d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82145df7bda52661f317964acebcbd6da9c4b0827804ee7ecc00cb2c59078bc0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-12-14T09:00:41Z",
    "title_canon_sha256": "6ee8a461219479270e9c9fc0e57982f0ccaa7bd1c9840d94f76f3803b136f5c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.04539",
    "kind": "arxiv",
    "version": 4
  }
}