Pith Number

pith:BHS7FHX6

pith:2025:BHS7FHX6GY4F3ZG6O7EM2DJBGN

not attested not anchored not stored refs pending

Generalized Fermat's principle and Snell's law for cone structures and applications

Enrique Pend\'as-Recondo, Miguel \'Angel Javaloyes, Miguel S\'anchez, Steen Markvorsen

arxiv:2509.26492 v2 · 2025-09-30 · math.DG · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BHS7FHX6GY4F3ZG6O7EM2DJBGN}

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.

Cited by

1 paper in Pith

On the formulations of the Fermat principle in general relativity and beyond

Receipt and verification

First computed	2026-06-23T01:12:47.501462Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09e5f29efe36385de4de77c8cd0d213377789f47dda855ab70194f95baad7827

Aliases

arxiv: 2509.26492 · arxiv_version: 2509.26492v2 · doi: 10.48550/arxiv.2509.26492 · pith_short_12: BHS7FHX6GY4F · pith_short_16: BHS7FHX6GY4F3ZG6 · pith_short_8: BHS7FHX6

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/BHS7FHX6GY4F3ZG6O7EM2DJBGN \
  | 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: 09e5f29efe36385de4de77c8cd0d213377789f47dda855ab70194f95baad7827

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce4e7b77fb1c59ae6dcd6fe63e83538947ab8796931e3a406cdefa7fd432a971",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-09-30T16:35:54Z",
    "title_canon_sha256": "7c018008473da5de4561dfafeb9618d2d048597037d8958d23e11128d65a9ba7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.26492",
    "kind": "arxiv",
    "version": 2
  }
}