Pith Number

pith:CXY2QH2O

pith:2016:CXY2QH2ON2CDD7VZFYEQSABPWY

not attested not anchored not stored refs pending

All-Pairs 2-Reachability in $\mathcal{O}(n^{\omega}\log n)$ Time

Daniel Graf, Giuseppe F. Italiano, Loukas Georgiadis, Nikos Parotsidis, Przemys{\l}aw Uzna\'nski

arxiv:1612.08075 v2 · 2016-12-23 · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CXY2QH2ON2CDD7VZFYEQSABPWY}

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	2026-05-18T00:39:28.805401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15f1a81f4e6e8431feb92e0909002fb603b80de31c6b6f292675e4590c81e5cc

Aliases

arxiv: 1612.08075 · arxiv_version: 1612.08075v2 · doi: 10.48550/arxiv.1612.08075 · pith_short_12: CXY2QH2ON2CD · pith_short_16: CXY2QH2ON2CDD7VZ · pith_short_8: CXY2QH2O

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/CXY2QH2ON2CDD7VZFYEQSABPWY \
  | 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: 15f1a81f4e6e8431feb92e0909002fb603b80de31c6b6f292675e4590c81e5cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6ea67bc97cf4a9b1a1e9df8d2bc63c6c818f5a355a7d3576a412affd4c64c53",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2016-12-23T20:05:32Z",
    "title_canon_sha256": "a785a90490557ba1046cc387e7f8e53027578d07e01d878a6dc7fe82a5f42031"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08075",
    "kind": "arxiv",
    "version": 2
  }
}