Pith Number

pith:TQOVOAQK

pith:2026:TQOVOAQK4QNZVOLUXSOFXXRNLN

not attested not anchored not stored refs pending

Polarization-Dependent Photon Propagation, Quasinormal Modes, and Gravitational Lensing in Higher-Curvature Effective Theories

Takamasa Kanai

arxiv:2606.19773 v1 · 2026-06-18 · gr-qc · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TQOVOAQK4QNZVOLUXSOFXXRNLN}

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	2026-06-19T16:12:34.764685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c1d57020ae41b9ab974bc9c5bde2d5b7a21dcf48aa882cd153166c5c872e596

Aliases

arxiv: 2606.19773 · arxiv_version: 2606.19773v1 · doi: 10.48550/arxiv.2606.19773 · pith_short_12: TQOVOAQK4QNZ · pith_short_16: TQOVOAQK4QNZVOLU · pith_short_8: TQOVOAQK

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/TQOVOAQK4QNZVOLUXSOFXXRNLN \
  | 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: 9c1d57020ae41b9ab974bc9c5bde2d5b7a21dcf48aa882cd153166c5c872e596

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d10b5b92b9ff62fb89fb5fc5982b91bb0c92438f794c68d384940108645a1f8",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-06-18T04:13:51Z",
    "title_canon_sha256": "e06c3d63179f7d92d3f4d4a28fa699733047c6167531ee79cdd6183493f2bfa6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.19773",
    "kind": "arxiv",
    "version": 1
  }
}