Pith Number

pith:W74YAQ3T

pith:2023:W74YAQ3TJNXMFONRVYFGZRLU4A

not attested not anchored not stored refs pending

Characterization of cactus-expandable digraphs via doubly bidirectionally connected pairs

Hiroki Kodama

A digraph with a doubly bidirectionally connected pair admits no cactus expansion.

arxiv:2312.17327 v4 · 2023-12-28 · math.CO

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W74YAQ3TJNXMFONRVYFGZRLU4A}

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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.

Claims

C1strongest claim

If a digraph has a doubly bidirectionally connected pair, then no expansion of it is cactus.

C2weakest assumption

The definitions and prior result from Azuma et al. on cactus-expandability for digraphs without such pairs are taken as given and correctly applied to the converse case.

C3one line summary

If a digraph has a doubly bidirectionally connected pair, then no expansion of it is cactus.

Receipt and verification

First computed	2026-06-04T01:08:24.741280Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7f98043734b6ec2b9b1ae0a6cc574e01e58e729152f87d6773f82d89c70d7d4

Aliases

arxiv: 2312.17327 · arxiv_version: 2312.17327v4 · doi: 10.48550/arxiv.2312.17327 · pith_short_12: W74YAQ3TJNXM · pith_short_16: W74YAQ3TJNXMFONR · pith_short_8: W74YAQ3T

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/W74YAQ3TJNXMFONRVYFGZRLU4A \
  | 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: b7f98043734b6ec2b9b1ae0a6cc574e01e58e729152f87d6773f82d89c70d7d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6157897841c0198fd66dd61b196255501b3c465141d4f51f2bf37510a51cef63",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-12-28T19:05:12Z",
    "title_canon_sha256": "5acb77bacf408ac3f720375820420944e1f39de532960477c2c1952a1c2ba2c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.17327",
    "kind": "arxiv",
    "version": 4
  }
}