Pith Number

pith:FQOFQVTU

pith:2026:FQOFQVTU5EAAKTQFQNRXGFEZEB

not attested not anchored not stored refs pending

Breathing Black Hole Shadows in Modified Gravity (MOG)

Emmanuel T. Rodulfo, Nikko John Leo S. Lobos

arxiv:2602.21432 v3 · 2026-02-24 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FQOFQVTU5EAAKTQFQNRXGFEZEB}

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

2 papers in Pith

Post-Newtonian orbital mechanics around a black hole in modified gravity

Dynamical Black Hole Thermodynamics in Modified Gravity

Receipt and verification

First computed	2026-07-07T02:17:19.463409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c1c585674e900054e0583637314992067697ae7e4012db030e340ad1bfda1dc

Aliases

arxiv: 2602.21432 · arxiv_version: 2602.21432v3 · doi: 10.48550/arxiv.2602.21432 · pith_short_12: FQOFQVTU5EAA · pith_short_16: FQOFQVTU5EAAKTQF · pith_short_8: FQOFQVTU

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/FQOFQVTU5EAAKTQFQNRXGFEZEB \
  | 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: 2c1c585674e900054e0583637314992067697ae7e4012db030e340ad1bfda1dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a96abac05a3077e959a73b15217ed31df6e5ab673e91a623239e30da5d20abb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-02-24T23:22:30Z",
    "title_canon_sha256": "258579755437e437f1d46d6b4ba5ff976a9e4598956a9d03fda9443b31170262"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.21432",
    "kind": "arxiv",
    "version": 3
  }
}