Pith Number

pith:KF5Z2IGC

pith:2017:KF5Z2IGC2LXD2FPJEDS7CSAAUE

not attested not anchored not stored refs pending

Optimal Packings of Two to Four Equal Circles on Any Flat Torus

AnnaVictoria Ellsworth, Hanson Smith, Jennifer Kenkel, Madeline Brandt, William Dickinson

arxiv:1708.05395 v2 · 2017-08-17 · 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{KF5Z2IGC2LXD2FPJEDS7CSAAUE}

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	2026-05-17T23:46:22.093032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

517b9d20c2d2ee3d15e920e5f14800a128c85099d165efb4644a18a1ba83ca58

Aliases

arxiv: 1708.05395 · arxiv_version: 1708.05395v2 · doi: 10.48550/arxiv.1708.05395 · pith_short_12: KF5Z2IGC2LXD · pith_short_16: KF5Z2IGC2LXD2FPJ · pith_short_8: KF5Z2IGC

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/KF5Z2IGC2LXD2FPJEDS7CSAAUE \
  | 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: 517b9d20c2d2ee3d15e920e5f14800a128c85099d165efb4644a18a1ba83ca58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ca241bbf9ccec4f70284e2df73de6ff5c1c15f879c57a216efdbac6c23cb063",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2017-08-17T18:04:53Z",
    "title_canon_sha256": "e457b10f7ff2cfea834fcd5f512696940c2c72667e798b41767337b9220908d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.05395",
    "kind": "arxiv",
    "version": 2
  }
}