Pith Number

pith:OW3FHKXG

pith:2025:OW3FHKXGUU5ZVKAU6OLFKTWQQW

not attested not anchored not stored refs pending

A Dynamic, Self-balancing k-d Tree

Russell A. Brown

A k-d tree can be made dynamic and self-balancing with specialized insertion, deletion, and rebalancing algorithms that preserve its alternating-dimension invariant.

arxiv:2509.08148 v18 · 2025-09-09 · cs.DS

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\usepackage{pith}
\pithnumber{OW3FHKXGUU5ZVKAU6OLFKTWQQW}

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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

It is possible to build a dynamic k-d tree that self-balances when necessary after insertion or deletion of each k-dimensional datum.

C2weakest assumption

Rebalancing steps can be designed that restore balance after each update while strictly preserving the k-d tree's alternating-dimension partitioning invariant at every node.

C3one line summary

The paper introduces insertion, deletion, and rebalancing algorithms for a dynamic self-balancing k-d tree and measures their performance.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-27T01:04:50.383831Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

75b653aae6a53b9aa814f396554ed085ab91f7f75660df3fd97bd9a4b9b173bc

Aliases

arxiv: 2509.08148 · arxiv_version: 2509.08148v18 · doi: 10.48550/arxiv.2509.08148 · pith_short_12: OW3FHKXGUU5Z · pith_short_16: OW3FHKXGUU5ZVKAU · pith_short_8: OW3FHKXG

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/OW3FHKXGUU5ZVKAU6OLFKTWQQW \
  | 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: 75b653aae6a53b9aa814f396554ed085ab91f7f75660df3fd97bd9a4b9b173bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c90a977119d9508b192b0746da916f91a1459c9f31593935cf6e7475cf6ae8e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2025-09-09T21:10:15Z",
    "title_canon_sha256": "6b873678e0be5324c3c509e00dafd1c8041d6ee7f5843579781abf8f2f90e20c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.08148",
    "kind": "arxiv",
    "version": 18
  }
}