Pith Number

pith:RXJO4JAT

pith:2026:RXJO4JATSRKFG7YHR2SBWWPULH

not attested not anchored not stored refs resolved

The KnotMosaics Package for SageMath

Allison K. Henrich, Andrew R. Tawfeek, Mary Y. Deng, Sean H. Kawano

KnotMosaics package represents knot mosaics as matrices of tile labels to validate and analyze them in SageMath.

arxiv:2605.14189 v1 · 2026-05-13 · math.GT

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\pithnumber{RXJO4JATSRKFG7YHR2SBWWPULH}

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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

The package represents an n-mosaic as a matrix of standard tile labels and implements the local connectivity rules needed to validate mosaics, trace strands and components, compute planar diagram codes, generate random examples, and construct rational tangle mosaics.

C2weakest assumption

That the chosen tile labels and local connectivity rules faithfully reproduce the standard mathematical definition of knot mosaics from the existing literature.

C3one line summary

KnotMosaics is a SageMath package that constructs, validates, and analyzes knot mosaic diagrams while linking them to existing knot invariant computations.

References

16 extracted · 16 resolved · 0 Pith anchors

[1] Bounds on mosaic knots 2014

[2] On upper bounds for toroidal mosaic numbers 2013

[3] An Enumeration of Knots and Links, and Some of Their Algebraic Properties 1970 · doi:10.1016/b978-0-08-012975-4.50034-

[4] Taming Wild Knots with Recursive Mosaics 2025

[5] Virtual mosaic knot theory 2020

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:11.155712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8dd2ee24139454537f078ea41b59f459c8c1efccee4b47acb2e43ca99b2af30d

Aliases

arxiv: 2605.14189 · arxiv_version: 2605.14189v1 · doi: 10.48550/arxiv.2605.14189 · pith_short_12: RXJO4JATSRKF · pith_short_16: RXJO4JATSRKFG7YH · pith_short_8: RXJO4JAT

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/RXJO4JATSRKFG7YHR2SBWWPULH \
  | 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: 8dd2ee24139454537f078ea41b59f459c8c1efccee4b47acb2e43ca99b2af30d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6eeaf0dbfaa16af540ccdd5500f327bd5917e85930e41bbb0e0857eaf679776e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-13T23:11:35Z",
    "title_canon_sha256": "0cd1ed247ac122672c70bccd2544965055e32e7919f3fa0889aae0de9e28b0ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14189",
    "kind": "arxiv",
    "version": 1
  }
}