Pith Number

pith:KIE3U3RH

pith:2015:KIE3U3RHRUE2FO2MYZGPQLCO7H

not attested not anchored not stored refs pending

Density upper bound for congruent and non-congruent hyperball packings generated by truncated regular simplex tilings

Jen\H{o} Szirmai

arxiv:1510.03208 v1 · 2015-10-12 · 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{KIE3U3RHRUE2FO2MYZGPQLCO7H}

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	2026-05-18T01:30:32.466571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5209ba6e278d09a2bb4cc64cf82c4ef9f8ab7afe602c999bf01dc9c96bcca270

Aliases

arxiv: 1510.03208 · arxiv_version: 1510.03208v1 · doi: 10.48550/arxiv.1510.03208 · pith_short_12: KIE3U3RHRUE2 · pith_short_16: KIE3U3RHRUE2FO2M · pith_short_8: KIE3U3RH

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/KIE3U3RHRUE2FO2MYZGPQLCO7H \
  | 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: 5209ba6e278d09a2bb4cc64cf82c4ef9f8ab7afe602c999bf01dc9c96bcca270

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2073de35adda2337ab540435f1055f491f08a2ca0c4c51f3ec308b33be56d84",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-10-12T10:04:04Z",
    "title_canon_sha256": "0194f7c0dfb05bf674864613e70c7718a0495402f7c2ef6533d20c7bb7025c09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03208",
    "kind": "arxiv",
    "version": 1
  }
}