Pith Number

pith:SD6UOVKQ

pith:2002:SD6UOVKQYEUGEGHMEL5QMZQL4D

not attested not anchored not stored refs pending

Improved bounds on the spectral gap above frustration free ground states of quantum spin chains

Shannon Starr, Wolfgang L Spitzer

arxiv:math-ph/0212029 v1 · 2002-12-10 · 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{SD6UOVKQYEUGEGHMEL5QMZQL4D}

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	2026-05-18T04:14:46.467370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90fd475550c1286218ec22fb06660be0de8ebe4555e5a79baae0fa82f3389f28

Aliases

arxiv: math-ph/0212029 · arxiv_version: math-ph/0212029v1 · doi: 10.48550/arxiv.math-ph/0212029 · pith_short_12: SD6UOVKQYEUG · pith_short_16: SD6UOVKQYEUGEGHM · pith_short_8: SD6UOVKQ

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/SD6UOVKQYEUGEGHMEL5QMZQL4D \
  | 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: 90fd475550c1286218ec22fb06660be0de8ebe4555e5a79baae0fa82f3389f28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f2986dc5eac54377fbd172ba51cae94f8f38b69927417ff88589e57c067ce99",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2002-12-10T07:27:04Z",
    "title_canon_sha256": "9bc007adf6004d5a2ddcb7fa30b900b27134aaffa08879a7800d2d2d4907bab5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0212029",
    "kind": "arxiv",
    "version": 1
  }
}