Pith Number

pith:X5Z5P2HK

pith:2024:X5Z5P2HKQNJNU7LQBBWQXGO3GC

not attested not anchored not stored refs pending

The Tammes Problem in $\mathbb{R}^{n}$ and Linear Programming Method

Qun Mo, Yanlu Lian, Yu Xia

arxiv:2411.16038 v1 · 2024-11-25 · 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{X5Z5P2HKQNJNU7LQBBWQXGO3GC}

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	2026-07-05T09:40:02.951554Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf73d7e8ea8352da7d70086d0b99db30b38fd61e30204179bf3045275e47c050

Aliases

arxiv: 2411.16038 · arxiv_version: 2411.16038v1 · doi: 10.48550/arxiv.2411.16038 · pith_short_12: X5Z5P2HKQNJN · pith_short_16: X5Z5P2HKQNJNU7LQ · pith_short_8: X5Z5P2HK

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/X5Z5P2HKQNJNU7LQBBWQXGO3GC \
  | 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: bf73d7e8ea8352da7d70086d0b99db30b38fd61e30204179bf3045275e47c050

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66d8658f344f8a05db66ab6b7e3418a6eaa021e4227331a0b6f74a7de1171396",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2024-11-25T02:02:41Z",
    "title_canon_sha256": "022509a7cbad0cb2b2148a391b7b640eeb5ea0fb328b08fdb8f05f7da628614c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.16038",
    "kind": "arxiv",
    "version": 1
  }
}