Pith Number

pith:ZESDPELF

pith:2026:ZESDPELFNKO453HHLFC4VLPDGN

not attested not anchored not stored refs pending

Perturbations of black holes in mass-varying massive gravity

De-Jun Wu

arxiv:2607.17046 v1 · 2026-07-19 · 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{ZESDPELFNKO453HHLFC4VLPDGN}

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	2026-07-21T01:21:12.109661Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9243791656a9dceece75945caade33356a43e95aabdf1f6ae26e9da953104c7

Aliases

arxiv: 2607.17046 · arxiv_version: 2607.17046v1 · doi: 10.48550/arxiv.2607.17046 · pith_short_12: ZESDPELFNKO4 · pith_short_16: ZESDPELFNKO453HH · pith_short_8: ZESDPELF

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/ZESDPELFNKO453HHLFC4VLPDGN \
  | 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: c9243791656a9dceece75945caade33356a43e95aabdf1f6ae26e9da953104c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f54a55ee44b08b2dead3cc17792b4bb0a14138ed9f023e6b0751c3406a62583",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-07-19T03:22:26Z",
    "title_canon_sha256": "81d063fb71796e77343eb5b6dac8886e02d782884274d6325461c49bd27b043c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.17046",
    "kind": "arxiv",
    "version": 1
  }
}