Pith Number

pith:PPRYGZZY

pith:2026:PPRYGZZY447DS3KBBUHVTVV6IC

not attested not anchored not stored refs pending

On converse invariant trees of diameter four

Fernando Afonso, Lucas Colucci, T\'assio Naia

arxiv:2606.24739 v1 · 2026-06-23 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PPRYGZZY447DS3KBBUHVTVV6IC}

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	2026-06-24T01:15:40.619976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7be3836738e73e396d410d0f59d6be4086ec22f4eceeb6dc05ca796f196af53b

Aliases

arxiv: 2606.24739 · arxiv_version: 2606.24739v1 · doi: 10.48550/arxiv.2606.24739 · pith_short_12: PPRYGZZY447D · pith_short_16: PPRYGZZY447DS3KB · pith_short_8: PPRYGZZY

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/PPRYGZZY447DS3KBBUHVTVV6IC \
  | 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: 7be3836738e73e396d410d0f59d6be4086ec22f4eceeb6dc05ca796f196af53b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "910dffb5082468f08ac72b4b2002835fdafe6fc3c5f21926d435d6e39deb48a5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-23T16:01:43Z",
    "title_canon_sha256": "2455944c916cd17eb3c1b0e6fac75a309b3b2aea48a8684ba3e072ba516c8363"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24739",
    "kind": "arxiv",
    "version": 1
  }
}