Pith Number

pith:6Y54UTQR

pith:2019:6Y54UTQRSGODZCEG3VC7G2UV5U

not attested not anchored not stored refs pending

Dual linear programming bounds for sphere packing via modular forms

Henry Cohn, Nicholas Triantafillou

arxiv:1909.04772 v2 · 2019-09-10 · 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{6Y54UTQRSGODZCEG3VC7G2UV5U}

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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.

Cited by

1 paper in Pith

Cusp Form Dimensions, Lattice Uniqueness, and LP Sharpness for Sphere Packing in Dimensions 8 and 24

Receipt and verification

First computed	2026-07-05T02:33:15.403997Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f63bca4e11919c3c8886dd45f36a95ed18191516f9977e36918f647a6211774b

Aliases

arxiv: 1909.04772 · arxiv_version: 1909.04772v2 · doi: 10.48550/arxiv.1909.04772 · pith_short_12: 6Y54UTQRSGOD · pith_short_16: 6Y54UTQRSGODZCEG · pith_short_8: 6Y54UTQR

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/6Y54UTQRSGODZCEG3VC7G2UV5U \
  | 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: f63bca4e11919c3c8886dd45f36a95ed18191516f9977e36918f647a6211774b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00ec9ed8a18a6d4d07611e6dd6aaf5131c505d393ababf2fca319c9aca03b9e6",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2019-09-10T21:55:27Z",
    "title_canon_sha256": "d67a824497108f2dbae000f4cb3667995c16308dd5be6591f33801a79b3fd71a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.04772",
    "kind": "arxiv",
    "version": 2
  }
}