Pith Number

pith:DGSGFT6V

pith:2013:DGSGFT6VGSR2NXP4ZP2W7LOEJJ

not attested not anchored not stored refs pending

Apollonian Ball Packings and Stacked Polytopes

Hao Chen

arxiv:1306.2515 v2 · 2013-06-11 · math.MG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DGSGFT6VGSR2NXP4ZP2W7LOEJJ}

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	2026-05-18T01:13:29.015154Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19a462cfd534a3a6ddfccbf56fadc44a669a4a64052b2d2db9c53395706a2c04

Aliases

arxiv: 1306.2515 · arxiv_version: 1306.2515v2 · doi: 10.48550/arxiv.1306.2515 · pith_short_12: DGSGFT6VGSR2 · pith_short_16: DGSGFT6VGSR2NXP4 · pith_short_8: DGSGFT6V

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/DGSGFT6VGSR2NXP4ZP2W7LOEJJ \
  | 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: 19a462cfd534a3a6ddfccbf56fadc44a669a4a64052b2d2db9c53395706a2c04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04ef09b087c90943bf59c00ffe77d56567dd6f8db95021de47209c8977fdbd08",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-06-11T13:24:46Z",
    "title_canon_sha256": "8d3eb8e9fe5d76f0a575a69a4843f62d7af0e4e189727d71db8ba0a97f37556c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.2515",
    "kind": "arxiv",
    "version": 2
  }
}