Pith Number

pith:UFBZR5UI

pith:2020:UFBZR5UIZT2UAUOGVHNVPEMURK

not attested not anchored not stored refs pending

Explicit formulae for geodesics in left invariant sub-Finsler problems on Heisenberg groups via convex trigonometry

L.V. Lokutsievskiy

arxiv:2005.08941 v2 · 2020-05-15 · math.OC · math.DG

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UFBZR5UIZT2UAUOGVHNVPEMURK}

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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.

Cited by

1 paper in Pith

Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups

Receipt and verification

First computed	2026-07-05T01:34:54.217428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a14398f688ccf54051c6a9db5791948aa89f2857cd02c58fce7777a1728013c6

Aliases

arxiv: 2005.08941 · arxiv_version: 2005.08941v2 · doi: 10.48550/arxiv.2005.08941 · pith_short_12: UFBZR5UIZT2U · pith_short_16: UFBZR5UIZT2UAUOG · pith_short_8: UFBZR5UI

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/UFBZR5UIZT2UAUOGVHNVPEMURK \
  | 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: a14398f688ccf54051c6a9db5791948aa89f2857cd02c58fce7777a1728013c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19afeb47c19e0b330ac5339c771b215b46ce6b515d6c8aa581bb20c12524daad",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2020-05-15T19:15:50Z",
    "title_canon_sha256": "3170e91e40ef5ecf0917326bb209dff02e8087737d2aeb16e23af5fa2a10b7a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2005.08941",
    "kind": "arxiv",
    "version": 2
  }
}