Pith Number

pith:IJJLYIUE

pith:2018:IJJLYIUEYHXFTL2SH7MLSK5GZQ

not attested not anchored not stored refs pending

Apollonian sets in taxicab geometry

Aaron Fish, Anna Miller, Dylan Helliwell, Eric Bahuaud, Freddy Nungaray, Julian Tiffay, Nico Velez, Shana Crawford, Suki Shergill

arxiv:1809.07487 v1 · 2018-09-20 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IJJLYIUEYHXFTL2SH7MLSK5GZQ}

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	2026-05-18T00:05:16.138021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4252bc2284c1ee59af523fd8b92ba6cc3ffa42f3846e98882e8e9e76eecdc5e3

Aliases

arxiv: 1809.07487 · arxiv_version: 1809.07487v1 · doi: 10.48550/arxiv.1809.07487 · pith_short_12: IJJLYIUEYHXF · pith_short_16: IJJLYIUEYHXFTL2S · pith_short_8: IJJLYIUE

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/IJJLYIUEYHXFTL2SH7MLSK5GZQ \
  | 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: 4252bc2284c1ee59af523fd8b92ba6cc3ffa42f3846e98882e8e9e76eecdc5e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "157c1c900ab34cc9f021d97d1acbf11dd3151157123aad2955f77314c63f2a22",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2018-09-20T06:19:59Z",
    "title_canon_sha256": "0dd13c4b68b650227508beeb32b7c90b7ee8b5749d0e5117bf6dd23b9baace18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.07487",
    "kind": "arxiv",
    "version": 1
  }
}