Pith Number

pith:MBLE2KNC

pith:2026:MBLE2KNC42HKB7Q4AZ2XID4OGI

not attested not anchored not stored refs pending

Minimal Generating Sets of Singular Reidemeister Moves and Their Classification

Noboru Ito, Yuichiro Iwamoto

Singular Reidemeister moves admit exactly 96 distinct inclusion-minimal generating sets once classical moves are fixed.

arxiv:2604.05597 v2 · 2026-04-07 · math.GT

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\pithnumber{MBLE2KNC42HKB7Q4AZ2XID4OGI}

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3 Author claim open · sign in to claim

4 Citations open

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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

starting from a minimal generating set of ordinary Reidemeister moves of types I--III, we prove that the singular moves admit exactly 96 distinct inclusion-minimal generating sets, and that these exhaust all possibilities.

C2weakest assumption

The newly introduced invariant, constructed via projection to self-singular links, correctly distinguishes the two families of type IV moves and supplies a genuine obstruction to generating type V from types I--IV.

C3one line summary

There are exactly 96 inclusion-minimal generating sets of oriented singular Reidemeister moves and 8 in the unoriented case.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-06-12T01:09:27.424212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60564d29a2e68ea0fe1c0675740f8e3220378635a7177b9954d53d4d995a7069

Aliases

arxiv: 2604.05597 · arxiv_version: 2604.05597v2 · doi: 10.48550/arxiv.2604.05597 · pith_short_12: MBLE2KNC42HK · pith_short_16: MBLE2KNC42HKB7Q4 · pith_short_8: MBLE2KNC

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/MBLE2KNC42HKB7Q4AZ2XID4OGI \
  | 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: 60564d29a2e68ea0fe1c0675740f8e3220378635a7177b9954d53d4d995a7069

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2856e41259f2793a663c2d219fdc1ba2150a995d0d8d2b3c4ee8420ff29ba62",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-04-07T08:47:11Z",
    "title_canon_sha256": "10fe2d48a201fa17795e47db3738b5e8f34e7dc218ef5d0b1be163c22e7ef02f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.05597",
    "kind": "arxiv",
    "version": 2
  }
}