Pith Number

pith:P5RX55SJ

pith:2026:P5RX55SJ45HQSGOJMSFSVJLRHS

not attested not anchored not stored refs pending

Refraction laws in spatio-temporal media

Cristian E. Guti\'errez, Eric Stachura

arxiv:2608.03995 v1 · 2026-08-04 · math.AP · math-ph · math.MP · physics.optics

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P5RX55SJ45HQSGOJMSFSVJLRHS}

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.

Receipt and verification

First computed	2026-08-05T01:37:39.677691Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f637ef649e74f0919c9648b2aa5713ca2da7a078015b8210075ca6f07fde194

Aliases

arxiv: 2608.03995 · arxiv_version: 2608.03995v1 · doi: 10.48550/arxiv.2608.03995 · pith_short_12: P5RX55SJ45HQ · pith_short_16: P5RX55SJ45HQSGOJ · pith_short_8: P5RX55SJ

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/P5RX55SJ45HQSGOJMSFSVJLRHS \
  | 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: 7f637ef649e74f0919c9648b2aa5713ca2da7a078015b8210075ca6f07fde194

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecbd9884d09adae4c764217570cd7f2d24492df9d2749be91af29a7212b8feee",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "physics.optics"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-04T17:55:18Z",
    "title_canon_sha256": "8fa18307a8705371ecdedb558c793344f1418663eed05400bc15823ca6755f69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.03995",
    "kind": "arxiv",
    "version": 1
  }
}