Pith Number

pith:GLOZBX4D

pith:2026:GLOZBX4DBJPW54Y3MTPBTCFR7Q

not attested not anchored not stored refs pending

Anisotropic isoperimetric double tilings of the plane

Emanuele Paolini, Francesco Nobili, Matteo Novaga

arxiv:2607.10636 v1 · 2026-07-12 · math.AP · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GLOZBX4DBJPW54Y3MTPBTCFR7Q}

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	2026-07-14T01:21:25.022653Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32dd90df830a5f6ef31b64de1988b1fc1760a53925fd17ed07146ce5e20bcb73

Aliases

arxiv: 2607.10636 · arxiv_version: 2607.10636v1 · doi: 10.48550/arxiv.2607.10636 · pith_short_12: GLOZBX4DBJPW · pith_short_16: GLOZBX4DBJPW54Y3 · pith_short_8: GLOZBX4D

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/GLOZBX4DBJPW54Y3MTPBTCFR7Q \
  | 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: 32dd90df830a5f6ef31b64de1988b1fc1760a53925fd17ed07146ce5e20bcb73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58fd2a6c1d9f35f807870e5049ef75f0d4406d941048dd6049d22fac4555a782",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-12T08:09:11Z",
    "title_canon_sha256": "5550d7385c5ddd41f0adb7e2f317233b90254aa3e977b0cc4dd32dd3e6f0be97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10636",
    "kind": "arxiv",
    "version": 1
  }
}