Pith Number

pith:HYAT6AVP

pith:2018:HYAT6AVP4EZRPSD6B7ACT6RK6R

not attested not anchored not stored refs pending

Asymptotic Linear Programming Lower Bounds for the Energy of Minimizing Riesz and Gauss Configurations

Douglas P. Hardin, Edward B. Saff, Timothy J. Michaels

arxiv:1804.05237 v1 · 2018-04-14 · 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{HYAT6AVP4EZRPSD6B7ACT6RK6R}

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	2026-05-17T23:53:31.273281Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e013f02afe13317c87e0fc029fa2af448882bb3881088c40d5a64aca0412e4a

Aliases

arxiv: 1804.05237 · arxiv_version: 1804.05237v1 · doi: 10.48550/arxiv.1804.05237 · pith_short_12: HYAT6AVP4EZR · pith_short_16: HYAT6AVP4EZRPSD6 · pith_short_8: HYAT6AVP

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/HYAT6AVP4EZRPSD6B7ACT6RK6R \
  | 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: 3e013f02afe13317c87e0fc029fa2af448882bb3881088c40d5a64aca0412e4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d1ab03a0e7655c7b558c68fec161418c4ba3d0a43c09f32c6a51ce1d98f9b00",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2018-04-14T15:19:51Z",
    "title_canon_sha256": "9affd3b0cf09b8ec51e6840f03796b7a2c5a4036080658c0bd75eff24dd69a48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.05237",
    "kind": "arxiv",
    "version": 1
  }
}