Pith Number

pith:3FZZB6SI

pith:2025:3FZZB6SIGRBIGTMB33F2DXFQ7W

not attested not anchored not stored refs pending

A Unified Framework for High-Dimensional Pure Root Lattices, Sphere Packing, and Cosmological Implications

C D MacDonald, S R MacDonald

arxiv:2502.09820 v1 · 2025-02-13 · physics.gen-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3FZZB6SIGRBIGTMB33F2DXFQ7W}

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	2026-07-05T10:34:42.490881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d97390fa483442834d81decba1dcb0fd886cff70adb3ad838b3695c79b5b668f

Aliases

arxiv: 2502.09820 · arxiv_version: 2502.09820v1 · doi: 10.48550/arxiv.2502.09820 · pith_short_12: 3FZZB6SIGRBI · pith_short_16: 3FZZB6SIGRBIGTMB · pith_short_8: 3FZZB6SI

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/3FZZB6SIGRBIGTMB33F2DXFQ7W \
  | 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: d97390fa483442834d81decba1dcb0fd886cff70adb3ad838b3695c79b5b668f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8935a07dc8d358210eecef1f73be66ede12959dc926a6e95cbc8b0dc6387214f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.gen-ph",
    "submitted_at": "2025-02-13T23:33:36Z",
    "title_canon_sha256": "06929b4ee1280b40ffacbd4fb373c1385d80639e803b94cbd77a6db26450fc80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.09820",
    "kind": "arxiv",
    "version": 1
  }
}