Pith Number

pith:GGRZXPC3

pith:2016:GGRZXPC3R6YFBCVZDCOGLBJ7QW

not attested not anchored not stored refs pending

Optimal stretching for lattice points and eigenvalues

Richard Laugesen, Shiya Liu

arxiv:1609.06172 v2 · 2016-09-05 · math.MG · math.NT · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GGRZXPC3R6YFBCVZDCOGLBJ7QW}

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	2026-05-18T00:35:55.570328Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31a39bbc5b8fb0508ab9189c65853f859253b0c3c4def84c2967c984461cc512

Aliases

arxiv: 1609.06172 · arxiv_version: 1609.06172v2 · doi: 10.48550/arxiv.1609.06172 · pith_short_12: GGRZXPC3R6YF · pith_short_16: GGRZXPC3R6YFBCVZ · pith_short_8: GGRZXPC3

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/GGRZXPC3R6YFBCVZDCOGLBJ7QW \
  | 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: 31a39bbc5b8fb0508ab9189c65853f859253b0c3c4def84c2967c984461cc512

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9cdb025c69d1453a7ed6acb1cf301aa43fee8471f4290eee0f4421115c38c74",
    "cross_cats_sorted": [
      "math.NT",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-09-05T23:26:59Z",
    "title_canon_sha256": "6ebdd9a1efd1fa18f4410fcb92034b975492d4f6dae1b49d8607f9f936df0c6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06172",
    "kind": "arxiv",
    "version": 2
  }
}