Pith Number

pith:PHSO37M2

pith:2017:PHSO37M2OR6YHYYXMMRXTT73W5

not attested not anchored not stored refs pending

Closure Properties in the Class of Multiple Context Free Groups

Davide Spriano, Robert P. Kropholler

arxiv:1709.02478 v2 · 2017-09-07 · 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{PHSO37M2OR6YHYYXMMRXTT73W5}

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	2026-05-17T23:56:34.429880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79e4edfd9a747d83e317632379cffbb7682f9ca5a02931fea2ac3febc74eb630

Aliases

arxiv: 1709.02478 · arxiv_version: 1709.02478v2 · doi: 10.48550/arxiv.1709.02478 · pith_short_12: PHSO37M2OR6Y · pith_short_16: PHSO37M2OR6YHYYX · pith_short_8: PHSO37M2

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/PHSO37M2OR6YHYYXMMRXTT73W5 \
  | 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: 79e4edfd9a747d83e317632379cffbb7682f9ca5a02931fea2ac3febc74eb630

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5592f23f3a52285acb41f1288b707c1ef9592eb75b350c49afd03c1ba05956d5",
    "cross_cats_sorted": [
      "cs.FL"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-09-07T22:37:34Z",
    "title_canon_sha256": "50db844ca25e1a579f1610310346167a0f409d3b0106ae64b5e19da9e6e6d5eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.02478",
    "kind": "arxiv",
    "version": 2
  }
}