Pith Number

pith:5MZT7UF4

pith:2026:5MZT7UF4RO7HKBDMZZBGFUUPVE

not attested not anchored not stored refs resolved

Fast Leaf-to-Ancestor Minimum Query in the Oracle Model

Aleksandr Levin, Aleksey Upirvitskiy

A static data structure preprocesses a rooted tree in O(n log h) oracle comparisons to answer any leaf-to-ancestor minimum query in O(1) time with no comparisons at query time.

arxiv:2605.14112 v1 · 2026-05-13 · cs.DS · cs.CC

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\usepackage{pith}
\pithnumber{5MZT7UF4RO7HKBDMZZBGFUUPVE}

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

We give a static data structure that, after O(n log h) preprocessing time, space, and oracle calls, answers any leaf-to-ancestor query in O(1) worst-case time with zero oracle calls at query time. The preprocessing oracle-comparison bound is tight in the deterministic comparison model.

C2weakest assumption

The input is a rooted tree whose edge (or node) weights admit a total order via a deterministic tie-breaking rule when the comparison oracle returns equality; the oracle is consistent across all calls.

C3one line summary

A data structure preprocesses a rooted weighted tree in O(n log h) time and space using comparisons to support O(1)-time leaf-to-ancestor minimum queries with zero oracle calls at query time.

References

3 extracted · 3 resolved · 0 Pith anchors

[1] arXiv:2105.01864 [cs.DS] (2021).https://arxiv.org/abs/2105.01864 2021

[2] Algorithmica 18, 263–270 (1997).https://doi.org/10.1007/BF02526037 1997 · doi:10.1007/bf02526037

[3] Robustness of temporal logic specifications for continuous-time sig- nals 2004 · doi:10.1016/j.tcs

Receipt and verification

First computed	2026-05-17T23:39:11.988272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb333fd0bc8bbe75046cce4262d28fa936f5813e7f114ad982f6977a6320a27f

Aliases

arxiv: 2605.14112 · arxiv_version: 2605.14112v1 · doi: 10.48550/arxiv.2605.14112 · pith_short_12: 5MZT7UF4RO7H · pith_short_16: 5MZT7UF4RO7HKBDM · pith_short_8: 5MZT7UF4

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/5MZT7UF4RO7HKBDMZZBGFUUPVE \
  | 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: eb333fd0bc8bbe75046cce4262d28fa936f5813e7f114ad982f6977a6320a27f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6c1f97b3fa88ce5cca8684047218437a628d5adb46be19dc1b031f0ba88f803",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-13T20:56:02Z",
    "title_canon_sha256": "1a6e9383c73575af93683a11754bf79fb138f4ed0e689f435647779fda39149f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14112",
    "kind": "arxiv",
    "version": 1
  }
}