Pith Number

pith:2JKQ2DBZ

pith:2018:2JKQ2DBZIFQR3VM4DDFRNL3WR3

not attested not anchored not stored refs pending

Periodic structure of translational multi-tilings in the plane

Bochen Liu

arxiv:1809.03440 v2 · 2018-09-10 · math.CO · math.CA · math.MG · 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{2JKQ2DBZIFQR3VM4DDFRNL3WR3}

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	2026-07-05T00:13:37.089090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2550d0c3941611dd59c18cb16af768ef8819669af66817f1e0678117cd0f84a

Aliases

arxiv: 1809.03440 · arxiv_version: 1809.03440v2 · doi: 10.48550/arxiv.1809.03440 · pith_short_12: 2JKQ2DBZIFQR · pith_short_16: 2JKQ2DBZIFQR3VM4 · pith_short_8: 2JKQ2DBZ

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/2JKQ2DBZIFQR3VM4DDFRNL3WR3 \
  | 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: d2550d0c3941611dd59c18cb16af768ef8819669af66817f1e0678117cd0f84a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbfa445f2ed35bedcb87f8a8c250542f6bfb34b0d6f8a0570b9160a2a1717da1",
    "cross_cats_sorted": [
      "math.CA",
      "math.MG",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-09-10T16:28:33Z",
    "title_canon_sha256": "503323d662adc583dbf52fc72ec4ba3827012e41ff1919c865a07c4aae570254"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.03440",
    "kind": "arxiv",
    "version": 2
  }
}