Pith Number

pith:5O7TYT7L

pith:2013:5O7TYT7LD4HVT7ZHS5QWDODLVY

not attested not anchored not stored refs pending

Bounding ground state energy of Hopfield models

Mihailo Stojnic

arxiv:1306.3764 v1 · 2013-06-17 · math.OC · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5O7TYT7LD4HVT7ZHS5QWDODLVY}

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	2026-05-18T03:20:46.540075Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebbf3c4feb1f0f59ff27976161b86bae24fb68c3f0c06b8c7b996259cef89ec2

Aliases

arxiv: 1306.3764 · arxiv_version: 1306.3764v1 · doi: 10.48550/arxiv.1306.3764 · pith_short_12: 5O7TYT7LD4HV · pith_short_16: 5O7TYT7LD4HVT7ZH · pith_short_8: 5O7TYT7L

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/5O7TYT7LD4HVT7ZHS5QWDODLVY \
  | 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: ebbf3c4feb1f0f59ff27976161b86bae24fb68c3f0c06b8c7b996259cef89ec2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afe7e88279083466804f2ac20899addc8241507a389e46e8ad9151ae8554914f",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-06-17T08:25:50Z",
    "title_canon_sha256": "bd9b0b1239ed662812a5fb9b5d9f6fe967d65d03b0736385df8bd208fd204d71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3764",
    "kind": "arxiv",
    "version": 1
  }
}