Pith Number

pith:ZW5JFSYK

pith:2026:ZW5JFSYKQSE4C7EVQSALGC2O4N

not attested not anchored not stored refs resolved

On the Constructive Dimension Spectrum of Polynomials

Prajval Koul, Satyadev Nandakumar

Every polynomial curve has an effective dimension spectrum containing at least two points

arxiv:2605.13868 v1 · 2026-05-03 · math.GM

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\usepackage{pith}
\pithnumber{ZW5JFSYKQSE4C7EVQSALGC2O4N}

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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

we show that the dimension spectra of every polynomial curve contains at least two points. This answers an open question posed by Stull.

C2weakest assumption

The adaptation of classical real root-finding techniques to the effective dimension setting preserves the necessary properties and can be carried out constructively without hidden inconsistencies or unstated assumptions.

C3one line summary

The effective dimension spectrum of every polynomial curve contains at least two points, with the conjecture resolved for the subfamily of low-dimensional coefficient polynomials.

References

24 extracted · 24 resolved · 0 Pith anchors

[1] Adam Case and Jack H. Lutz. Mutual dimension. ACM Trans. Comput. Theory , 7(3):12:1--12:26, 2015. https://doi.org/10.1145/2786566 doi:10.1145/2786566 2015 · doi:10.1145/2786566

[2] Exercices de mathématique

[3] Algorithmic Randomness and Complexity 2008

[4] 2019 , isbn = 2019 · doi:10.1007/978-3-030-11298-1

[5] J. H. Lutz. Gales and the constructive dimension of individual sequences. In Proceedings of the 27th International Colloquium on Automata, Languages, and Programming , pages 902--913, 2000. Revised as 2000

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:15.605382Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdba92cb0a8489c17c958480b30b4ee3766909b91d6e74c51de05348b9d37552

Aliases

arxiv: 2605.13868 · arxiv_version: 2605.13868v1 · doi: 10.48550/arxiv.2605.13868 · pith_short_12: ZW5JFSYKQSE4 · pith_short_16: ZW5JFSYKQSE4C7EV · pith_short_8: ZW5JFSYK

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/ZW5JFSYKQSE4C7EVQSALGC2O4N \
  | 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: cdba92cb0a8489c17c958480b30b4ee3766909b91d6e74c51de05348b9d37552

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69a543178faf610c5438ac379dc9972104c6f5109d0987fc479393a07bbd8817",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2026-05-03T05:06:11Z",
    "title_canon_sha256": "20fbb403daaef89d073f7adc3bb1c2cc50739adea8aa0176415255a7cbdaa935"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13868",
    "kind": "arxiv",
    "version": 1
  }
}