Pith Number

pith:VKBOMWV7

pith:2013:VKBOMWV763AW2WQ7RC2G5UA5RV

not attested not anchored not stored refs pending

Fundamental domains for properly discontinuous affine groups

Ilia Smilga

arxiv:1303.3766 v2 · 2013-03-15 · 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{VKBOMWV763AW2WQ7RC2G5UA5RV}

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	2026-05-18T01:15:01.055186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa82e65abff6c16d5a1f88b46ed01d8d6ca2e4809beb6856a09dfc8c2cd275f1

Aliases

arxiv: 1303.3766 · arxiv_version: 1303.3766v2 · doi: 10.48550/arxiv.1303.3766 · pith_short_12: VKBOMWV763AW · pith_short_16: VKBOMWV763AW2WQ7 · pith_short_8: VKBOMWV7

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/VKBOMWV763AW2WQ7RC2G5UA5RV \
  | 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: aa82e65abff6c16d5a1f88b46ed01d8d6ca2e4809beb6856a09dfc8c2cd275f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c3d3b28374c1dd71855dff458e7fe67d0ba22aa512d9e969a985902f80605f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-03-15T13:22:09Z",
    "title_canon_sha256": "a01a3c29c6f2ec9590800fadd4a386d22973ac274ba576dabf2f09a8b12d6b2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.3766",
    "kind": "arxiv",
    "version": 2
  }
}