Pith Number

pith:LQGV2LNF

pith:2019:LQGV2LNFFCJKPZGFEYUUA3SDOF

not attested not anchored not stored refs pending

Solution of the 15 puzzle problem

Robert Hough, Yang Chu

arxiv:1908.07106 v1 · 2019-08-19 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LQGV2LNFFCJKPZGFEYUUA3SDOF}

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	2026-07-04T23:58:30.904052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c0d5d2da52892a7e4c52629406e4371589741cdd4b4cf63a5b828cc2587b6ef

Aliases

arxiv: 1908.07106 · arxiv_version: 1908.07106v1 · doi: 10.48550/arxiv.1908.07106 · pith_short_12: LQGV2LNFFCJK · pith_short_16: LQGV2LNFFCJKPZGF · pith_short_8: LQGV2LNF

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/LQGV2LNFFCJKPZGFEYUUA3SDOF \
  | 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: 5c0d5d2da52892a7e4c52629406e4371589741cdd4b4cf63a5b828cc2587b6ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93c93d5b476f6be279f84c4a69d724831576bbf268ddee2f468999751f910ce2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-08-19T23:43:30Z",
    "title_canon_sha256": "e596e019a678c853637babbd1e75422b26bcdedea81736462163542c4ebce24a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07106",
    "kind": "arxiv",
    "version": 1
  }
}