Pith Number

pith:OCAYXW3Y

pith:2015:OCAYXW3Y5PS5X755BIPHUB7BGD

not attested not anchored not stored refs pending

Knapsack in graph groups, HNN-extensions and amalgamated products

Georg Zetzsche, Markus Lohrey

arxiv:1509.05957 v1 · 2015-09-20 · math.GR · cs.FL

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OCAYXW3Y5PS5X755BIPHUB7BGD}

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	2026-05-18T01:32:36.258546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70818bdb78ebe5dbffbd0a1e7a07e130d7734b6585dbd21f3cb255ab3f800da0

Aliases

arxiv: 1509.05957 · arxiv_version: 1509.05957v1 · doi: 10.48550/arxiv.1509.05957 · pith_short_12: OCAYXW3Y5PS5 · pith_short_16: OCAYXW3Y5PS5X755 · pith_short_8: OCAYXW3Y

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/OCAYXW3Y5PS5X755BIPHUB7BGD \
  | 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: 70818bdb78ebe5dbffbd0a1e7a07e130d7734b6585dbd21f3cb255ab3f800da0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9928e73f5b0100376576ae45e3e094080abfad8cc1c28aa75e16f730b827906f",
    "cross_cats_sorted": [
      "cs.FL"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-20T02:18:11Z",
    "title_canon_sha256": "c3f5af61239a021ba39f173ff6f7ade6e12538cbf9deadadbce72053a92834ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05957",
    "kind": "arxiv",
    "version": 1
  }
}