Pith Number

pith:AOSALGHW

pith:2013:AOSALGHWXOAFZ3YUML6DAOLOR5

not attested not anchored not stored refs pending

Real reflections, commutators and cross-ratios in complex hyperbolic space

Julien Paupert, Pierre Will (IF)

arxiv:1312.3173 v1 · 2013-12-11 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AOSALGHWXOAFZ3YUML6DAOLOR5}

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	2026-05-18T03:05:00.290800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03a40598f6bb805cef1462fc30396e8f7e085dc2b9639b72cf1a0553180e9003

Aliases

arxiv: 1312.3173 · arxiv_version: 1312.3173v1 · doi: 10.48550/arxiv.1312.3173 · pith_short_12: AOSALGHWXOAF · pith_short_16: AOSALGHWXOAFZ3YU · pith_short_8: AOSALGHW

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/AOSALGHWXOAFZ3YUML6DAOLOR5 \
  | 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: 03a40598f6bb805cef1462fc30396e8f7e085dc2b9639b72cf1a0553180e9003

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e3ff3af6a55dfd6fbff307d8d135c2ef3737b96e98b0b16c24f5dbcbd633f42",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-12-11T14:08:31Z",
    "title_canon_sha256": "fa067693cf5ad732da14c9457b186df0fe60326e1003a03dfe93255af4dad808"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3173",
    "kind": "arxiv",
    "version": 1
  }
}