Pith Number

pith:ECYUOA37

pith:2026:ECYUOA37WTBRDRGRH57LTRSZ6U

not attested not anchored not stored refs pending

Generalized pseudo-product structures and finite type distributions via abnormal extremals

Boris Doubrov, Igor zelenko

Real-analytic distributions controllable by regular abnormal extremals have finite-dimensional symmetry algebras.

arxiv:2605.12307 v3 · 2026-05-12 · math.DG · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ECYUOA37WTBRDRGRH57LTRSZ6U}

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

In the real analytic category, distributions that are controllable by regular abnormal extremal trajectories, also known as singularly transitive, have finite-dimensional symmetries.

C2weakest assumption

The distributions are real analytic and the abnormal extremals are regular; the modified universal prolongation construction preserves the finiteness property without introducing infinite-dimensional symmetries.

C3one line summary

Generalized Tanaka prolongation criterion shows that singularly transitive distributions have finite-dimensional symmetries in the real analytic category.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:36.455689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20b147037fb4c311c4d13f7eb9c659f51c675ad03881488fa2535a669c2e7ea2

Aliases

arxiv: 2605.12307 · arxiv_version: 2605.12307v3 · doi: 10.48550/arxiv.2605.12307 · pith_short_12: ECYUOA37WTBR · pith_short_16: ECYUOA37WTBRDRGR · pith_short_8: ECYUOA37

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/ECYUOA37WTBRDRGRH57LTRSZ6U \
  | 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: 20b147037fb4c311c4d13f7eb9c659f51c675ad03881488fa2535a669c2e7ea2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ad8f9829bfced69eae67c3ea4edf7e95e23c6ea52832f9805cedec396687422",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-12T15:55:52Z",
    "title_canon_sha256": "2dfd70d1fc366d20adb049cbdce4e67258df3463a13dbcc076918b134396c762"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12307",
    "kind": "arxiv",
    "version": 3
  }
}