Pith Number

pith:GG37UTGD

pith:2010:GG37UTGDT62BI7PSOSNMFEGSN4

not attested not anchored not stored refs pending

Integral Points for Groups of Multiplicative Type

Dasheng Wei, Fei Xu

arxiv:1004.2613 v2 · 2010-04-15 · 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{GG37UTGDT62BI7PSOSNMFEGSN4}

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	2026-05-18T03:48:34.559050Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31b7fa4cc39fb4147df2749ac290d26f0e992bba113a5a1a397e6eb097b464ed

Aliases

arxiv: 1004.2613 · arxiv_version: 1004.2613v2 · doi: 10.48550/arxiv.1004.2613 · pith_short_12: GG37UTGDT62B · pith_short_16: GG37UTGDT62BI7PS · pith_short_8: GG37UTGD

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/GG37UTGDT62BI7PSOSNMFEGSN4 \
  | 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: 31b7fa4cc39fb4147df2749ac290d26f0e992bba113a5a1a397e6eb097b464ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9be27d80fa8b4fab5abc00b03c98a3abaf14d3b22ebeff5d5a7722de959d63a9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-04-15T12:00:41Z",
    "title_canon_sha256": "394924330b6c4f3cb030532814d45cd48345cc21d6c1f4dc939021fa7a95faf2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.2613",
    "kind": "arxiv",
    "version": 2
  }
}