Pith Number

pith:VYQJ4NIJ

pith:2011:VYQJ4NIJM27DAQ4ADS2GDZAEAT

not attested not anchored not stored refs pending

The size of the Universe according to the Poincare dodecahedral space hypothesis

Boudewijn F. Roukema, Tomasz A. Kazimierczak (Torun Centre for Astronomy UMK)

arxiv:1106.0727 v2 · 2011-06-03 · astro-ph.CO · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VYQJ4NIJM27DAQ4ADS2GDZAEAT}

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	2026-05-18T02:01:43.742242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae209e350966be3043801cb461e40404db3f98ae750e698a0ed2e35b3973a705

Aliases

arxiv: 1106.0727 · arxiv_version: 1106.0727v2 · doi: 10.48550/arxiv.1106.0727 · pith_short_12: VYQJ4NIJM27D · pith_short_16: VYQJ4NIJM27DAQ4A · pith_short_8: VYQJ4NIJ

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/VYQJ4NIJM27DAQ4ADS2GDZAEAT \
  | 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: ae209e350966be3043801cb461e40404db3f98ae750e698a0ed2e35b3973a705

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f637b9f9ecaeba88310547ffbda51a23d18c1fc975a1c55b133d7c38b957b868",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2011-06-03T19:03:48Z",
    "title_canon_sha256": "a380dec54a22e2408b5fb33a683db99838dee0705a9be25e4699efc211a957aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0727",
    "kind": "arxiv",
    "version": 2
  }
}