Pith Number

pith:PUMPAOCS

pith:2016:PUMPAOCSPCOVI42RDWUDRVY3SW

not attested not anchored not stored refs pending

On Gehring-Martin-Tan groups with an elliptic generator

Andrei Yu. Vesnin, Du\v{s}an D. Repov\v{s}

arxiv:1609.05044 v1 · 2016-09-16 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PUMPAOCSPCOVI42RDWUDRVY3SW}

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	2026-05-18T01:04:31.750947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d18f03852789d5473511da838d71b958eb957788474c6ef62cd6092a8dcd16b

Aliases

arxiv: 1609.05044 · arxiv_version: 1609.05044v1 · doi: 10.48550/arxiv.1609.05044 · pith_short_12: PUMPAOCSPCOV · pith_short_16: PUMPAOCSPCOVI42R · pith_short_8: PUMPAOCS

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/PUMPAOCSPCOVI42RDWUDRVY3SW \
  | 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: 7d18f03852789d5473511da838d71b958eb957788474c6ef62cd6092a8dcd16b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1af0382f0d23c13328abc39750d7f03cdb50406bf2b5520de1e70db0bb9e6b0",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-09-16T13:31:00Z",
    "title_canon_sha256": "0ed8b86ce2172d1c9c20689671f1330961b8618be20448c94bcd8728e911a30e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05044",
    "kind": "arxiv",
    "version": 1
  }
}