Pith Number

pith:PSHUURQH

pith:2025:PSHUURQHVZATBXT2HZCFSMBFYW

not attested not anchored not stored refs pending

A substitution lemma for multiple context-free languages

Andrew Duncan, Lisa Frenkel, Mengfan Lyu, Murray Elder

arxiv:2509.02117 v3 · 2025-09-02 · cs.FL · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PSHUURQHVZATBXT2HZCFSMBFYW}

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	2026-05-26T01:03:15.030757Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c8f4a4607ae4130de7a3e44593025c5b69049dff339d636e3b352e1c8869dc7

Aliases

arxiv: 2509.02117 · arxiv_version: 2509.02117v3 · doi: 10.48550/arxiv.2509.02117 · pith_short_12: PSHUURQHVZAT · pith_short_16: PSHUURQHVZATBXT2 · pith_short_8: PSHUURQH

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/PSHUURQHVZATBXT2HZCFSMBFYW \
  | 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: 7c8f4a4607ae4130de7a3e44593025c5b69049dff339d636e3b352e1c8869dc7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce23eecc11659efa22f306354d44d73b41ceac585733fa7116be3d1029a77d1a",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.FL",
    "submitted_at": "2025-09-02T09:13:14Z",
    "title_canon_sha256": "77903b61488326fb7c968414f3d8c6b464d0b8d0cf4a19a8defadf4ee94d3a13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.02117",
    "kind": "arxiv",
    "version": 3
  }
}