Pith Number

pith:JR32MUAV

pith:2026:JR32MUAVWS66OHSJEUSJOSRCBE

not attested not anchored not stored refs pending

A dual linear programming bound for sphere packing in dimension 36

Rifat Jumagulov

arxiv:2607.11319 v1 · 2026-07-13 · math.MG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JR32MUAVWS66OHSJEUSJOSRCBE}

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	2026-07-14T01:22:28.503098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c77a65015b4bde71e492524974a2209095a2db98d0d5f1d92b5b9420f76d761

Aliases

arxiv: 2607.11319 · arxiv_version: 2607.11319v1 · doi: 10.48550/arxiv.2607.11319 · pith_short_12: JR32MUAVWS66 · pith_short_16: JR32MUAVWS66OHSJ · pith_short_8: JR32MUAV

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/JR32MUAVWS66OHSJEUSJOSRCBE \
  | 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: 4c77a65015b4bde71e492524974a2209095a2db98d0d5f1d92b5b9420f76d761

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb82859a89f643ed0a99e08207d14b9f01a3b87bc81ee15201a38f79767b11dc",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-07-13T09:37:13Z",
    "title_canon_sha256": "a71d63868cc27e1ca80797cb1bafbc0022643a0579644245ed1088d89bbafb09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.11319",
    "kind": "arxiv",
    "version": 1
  }
}