Pith Number

pith:IRK25JSP

pith:2015:IRK25JSPJJZQEWZZKZTE5DGTRD

not attested not anchored not stored refs pending

Universal upper and lower bounds on energy of spherical designs

D. P. Hardin, E. B. Saff, M. M. Stoyanova, P. D. Dragnev, P. G. Boyvalenkov

arxiv:1509.07837 v1 · 2015-09-25 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IRK25JSPJJZQEWZZKZTE5DGTRD}

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	2026-05-18T01:32:01.839600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4455aea64f4a73025b3956664e8cd388e4b6bc02e7400736f6118dfe09ee4d4e

Aliases

arxiv: 1509.07837 · arxiv_version: 1509.07837v1 · doi: 10.48550/arxiv.1509.07837 · pith_short_12: IRK25JSPJJZQ · pith_short_16: IRK25JSPJJZQEWZZ · pith_short_8: IRK25JSP

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/IRK25JSPJJZQEWZZKZTE5DGTRD \
  | 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: 4455aea64f4a73025b3956664e8cd388e4b6bc02e7400736f6118dfe09ee4d4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7792da937949d6d1574a3785cea6fb0370b0c84cb493a815d0391d5db0a84f63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-09-25T19:12:10Z",
    "title_canon_sha256": "72acc84c2f21a1e9bd605575a88ba3929c609929a873a1362115aed453e6ba44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07837",
    "kind": "arxiv",
    "version": 1
  }
}