Pith Number

pith:6BJNFMFR

pith:2026:6BJNFMFRIB4VTX2HPQGOPTKCFN

not attested not anchored not stored refs resolved

Submetry onto one-dimensional space

Darya Sukhorebska

The Euclidean plane and two-dimensional sphere have their equidistant decompositions fully classified.

arxiv:2604.20562 v2 · 2026-04-22 · math.DG · math.MG

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\usepackage{pith}
\pithnumber{6BJNFMFRIB4VTX2HPQGOPTKCFN}

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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 provide the full classification of equidistant decomposition of a two-dimensional Euclidean plane and a two-dimensional sphere.

C2weakest assumption

The abstract assumes standard definitions of equidistant decomposition and the usual metrics on the plane and sphere suffice for a complete classification without additional constraints or exceptions.

C3one line summary

Full classification of equidistant decompositions of the 2D Euclidean plane and 2D sphere is provided.

References

1 extracted · 1 resolved · 0 Pith anchors

[1] [Ban82] V. Bangert. Sets with positive reach.Arch. Math., 38(1):54–57, 1982. [BBI01] D. Burago, Yu. Burago, and S. Ivanov.A Course in Metric Geometry, volume 33 Gradu- ate Studies in Mathematics.A Cou 1982

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T01:05:14.164412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f052d2b0b1407959df477c0ce7cd422b6093553394bebcaeca4943f6898075a9

Aliases

arxiv: 2604.20562 · arxiv_version: 2604.20562v2 · doi: 10.48550/arxiv.2604.20562 · pith_short_12: 6BJNFMFRIB4V · pith_short_16: 6BJNFMFRIB4VTX2H · pith_short_8: 6BJNFMFR

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/6BJNFMFRIB4VTX2HPQGOPTKCFN \
  | 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: f052d2b0b1407959df477c0ce7cd422b6093553394bebcaeca4943f6898075a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bbc9fc135030225d49195e185fb176b092051e1b48678a1befe9af6ef5445e7",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-04-22T13:43:33Z",
    "title_canon_sha256": "8a77cdd4896aef8c196ab9d4d224bac4a3ac2a469cd9e7c20149259a889733f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.20562",
    "kind": "arxiv",
    "version": 2
  }
}