Pith Number

pith:HVKKOTFY

pith:2025:HVKKOTFYDE7SDPCY6OGMSR2SXR

not attested not anchored not stored refs pending

Random close packing fraction of bidisperse discs: theoretical derivation

Raphael Blumenfeld

A disorder-guaranteeing theory using cell order distributions derives the highest possible random close packing fraction for bidisperse discs along with exact bounds.

arxiv:2509.20132 v4 · 2025-09-24 · cond-mat.soft · cond-mat.dis-nn · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HVKKOTFYDE7SDPCY6OGMSR2SXR}

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.

Claims

C1strongest claim

A disorder-guaranteeing theory is formulated here to derive the highest mathematically possible value of φ_RCP(p,D), using the concept of the cell order distribution. I also derive exact upper and lower bounds on this densest disordered packing fraction.

C2weakest assumption

The cell order distribution can be defined and used in a way that mathematically guarantees the packing remains fully disordered while still achieving the highest possible density.

C3one line summary

Derives the maximum random close packing fraction φ_RCP(p,D) for bidisperse discs via cell order distribution and supplies exact bounds.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Random close packing fraction of bidisperse discs: theoretical derivation

Receipt and verification

First computed	2026-05-26T01:02:27.859044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d54a74cb8193f21bc58f38cc94752bc748cff0c910220032c6dc06fe18984f6

Aliases

arxiv: 2509.20132 · arxiv_version: 2509.20132v4 · doi: 10.48550/arxiv.2509.20132 · pith_short_12: HVKKOTFYDE7S · pith_short_16: HVKKOTFYDE7SDPCY · pith_short_8: HVKKOTFY

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/HVKKOTFYDE7SDPCY6OGMSR2SXR \
  | 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: 3d54a74cb8193f21bc58f38cc94752bc748cff0c910220032c6dc06fe18984f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a3a8930ec416fdb691b67ebae18eaa0bd8bc38e3a04903df9ce33e7c092c0fa",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cond-mat.soft",
    "submitted_at": "2025-09-24T13:59:10Z",
    "title_canon_sha256": "52a91225d1d6fecec1d4d77cbc6aad89f9e894ec7ec80877d0e11348b4d0a2e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.20132",
    "kind": "arxiv",
    "version": 4
  }
}