Pith Number

pith:P34RC2JQ

pith:2018:P34RC2JQQRSN4EOL353QKR2O7X

not attested not anchored not stored refs pending

Eigenvalue optimisation on flat tori and lattice points in anisotropically expanding domains

Jean Lagac\'e

arxiv:1809.01469 v1 · 2018-09-05 · math.SP · math.AP · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P34RC2JQQRSN4EOL353QKR2O7X}

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	2026-05-18T00:06:27.557746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ef91169308464de11cbdf7705474efdd78ca6abf84111326edec58643f08770

Aliases

arxiv: 1809.01469 · arxiv_version: 1809.01469v1 · doi: 10.48550/arxiv.1809.01469 · pith_short_12: P34RC2JQQRSN · pith_short_16: P34RC2JQQRSN4EOL · pith_short_8: P34RC2JQ

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/P34RC2JQQRSN4EOL353QKR2O7X \
  | 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: 7ef91169308464de11cbdf7705474efdd78ca6abf84111326edec58643f08770

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f779983eb4e4775c547ac4459ead5d965c261b3036a4a24eb69e8a2f3e47eeb",
    "cross_cats_sorted": [
      "math.AP",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2018-09-05T12:59:51Z",
    "title_canon_sha256": "efdbbba2b61a503b1b7e4299ca6bd8cba91bd91244bd9c93f045fa2895790e48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.01469",
    "kind": "arxiv",
    "version": 1
  }
}