Pith Number

pith:GDQNVDZ7

pith:2026:GDQNVDZ74CGDUZDIKZPQRNF2B4

not attested not anchored not stored refs pending

Spectral and Isoperimetric Bounds on Flat Tori

Emanuel Milman

arxiv:2608.13052 v1 · 2026-08-13 · math.SP · math.FA · 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{GDQNVDZ74CGDUZDIKZPQRNF2B4}

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	2026-08-14T01:00:13.482614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30e0da8f3fe08c3a6468565f08b4ba0f0d0f54dcb6f76af3a534537dbbe752e7

Aliases

arxiv: 2608.13052 · arxiv_version: 2608.13052v1 · doi: 10.48550/arxiv.2608.13052 · pith_short_12: GDQNVDZ74CGD · pith_short_16: GDQNVDZ74CGDUZDI · pith_short_8: GDQNVDZ7

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/GDQNVDZ74CGDUZDIKZPQRNF2B4 \
  | 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: 30e0da8f3fe08c3a6468565f08b4ba0f0d0f54dcb6f76af3a534537dbbe752e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4de69f8112c6b347621aabd67e17325fd8560e1c64074e2180e0aab76868a55",
    "cross_cats_sorted": [
      "math.FA",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2026-08-13T10:16:43Z",
    "title_canon_sha256": "a57d63d2f853e77a3b34a6782bf47eb24efd9f2edfc0c1eeda6ff36f409ee0e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.13052",
    "kind": "arxiv",
    "version": 1
  }
}