Pith Number

pith:XQGROIN4

pith:2026:XQGROIN4ZWM5767FB7BUOODGZN

not attested not anchored not stored refs resolved

Taming Wild Knots with Mosaics

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

Infinite rooted tree mosaics represent wild knots with isolated wild points.

arxiv:2605.14185 v1 · 2026-05-13 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XQGROIN4ZWM5767FB7BUOODGZN}

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.

Claims

C1strongest claim

We extend Lomonaco and Kauffman's knot mosaic theory to represent a substantial subclass of wild knots that have isolated wild points. Our mosaics consist of infinite rooted trees with mosaics assigned to vertices and embedding functions governing connections.

C2weakest assumption

The assumption that the wild points are isolated and that the embedding functions can be chosen consistently so that the infinite tree actually produces a well-defined wild knot in 3-space without introducing extra entanglements or singularities.

C3one line summary

The authors introduce mosaic representations for wild knots with isolated wild points via infinite rooted trees carrying local mosaics and embedding functions, along with mosaic tangles and mosaic rigid vertex spatial graphs.

References

41 extracted · 41 resolved · 0 Pith anchors

[1] Alan and Dye, H 2014

[2] Quantum information processing , volume= 2013

[3] The Lomonaco-Kauffman Conjecture. , author=. Journal of Knot Theory & Its Ramifications , volume=

[4] Quantum Information Processing , volume= 2008

[5] Annals of Mathematics , volume= 1949

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:11.207092Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc0d1721bccd99dffbe50fc3473866cb7c631436e4513a41d2e5066c8136cb77

Aliases

arxiv: 2605.14185 · arxiv_version: 2605.14185v1 · doi: 10.48550/arxiv.2605.14185 · pith_short_12: XQGROIN4ZWM5 · pith_short_16: XQGROIN4ZWM5767F · pith_short_8: XQGROIN4

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/XQGROIN4ZWM5767FB7BUOODGZN \
  | 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: bc0d1721bccd99dffbe50fc3473866cb7c631436e4513a41d2e5066c8136cb77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c55e4d759b47b3086699e253622b86fb072018528eb28cb3e539c868100616e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-13T23:09:13Z",
    "title_canon_sha256": "d686b119d3cb4341f209ca94ae68cfc4c81b3a638295c4402192fb09d3226752"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14185",
    "kind": "arxiv",
    "version": 1
  }
}