Pith Number

pith:AYMH75H3

pith:2016:AYMH75H3TGYFQ4E47TLM6IKLUX

not attested not anchored not stored refs pending

Tight bounds on the maximum number of shortest unique substrings

Hideo Bannai, Masayuki Takeda, Shunsuke Inenaga, Takuya Mieno

arxiv:1609.07220 v2 · 2016-09-23 · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AYMH75H3TGYFQ4E47TLM6IKLUX}

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	2026-05-18T00:50:29.135950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06187ff4fb99b058709cfcd6cf214ba5f6f5c0e5e1258d414c4363d07862f259

Aliases

arxiv: 1609.07220 · arxiv_version: 1609.07220v2 · doi: 10.48550/arxiv.1609.07220 · pith_short_12: AYMH75H3TGYF · pith_short_16: AYMH75H3TGYFQ4E4 · pith_short_8: AYMH75H3

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/AYMH75H3TGYFQ4E47TLM6IKLUX \
  | 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: 06187ff4fb99b058709cfcd6cf214ba5f6f5c0e5e1258d414c4363d07862f259

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0529db4957da4672becd918b1c1aebde1bc2e0d9039c5f782fc5de8e7b01a3f1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2016-09-23T03:32:50Z",
    "title_canon_sha256": "73821665417e287709dbea92cd5bc1ee68a407e3a97947cda474dcfb6eafe62d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.07220",
    "kind": "arxiv",
    "version": 2
  }
}