Pith Number

pith:4N2DJY4T

pith:2026:4N2DJY4T23WKQ3QCWXAYIFGO2Q

not attested not anchored not stored refs pending

Echoes and quasinormal modes for static loop quantum black bounces

Guoyang Fu, Huajie Gong, Jian-Pin Wu, Qin Tan, Qiyuan Pan, Shulan Li

arxiv:2607.25738 v1 · 2026-07-28 · 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{4N2DJY4T23WKQ3QCWXAYIFGO2Q}

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	2026-07-29T01:25:59.938575Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e37434e393d6eca86e02b5c18414ced4098b2b1f5675eb9fd87063445e71e92d

Aliases

arxiv: 2607.25738 · arxiv_version: 2607.25738v1 · doi: 10.48550/arxiv.2607.25738 · pith_short_12: 4N2DJY4T23WK · pith_short_16: 4N2DJY4T23WKQ3QC · pith_short_8: 4N2DJY4T

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/4N2DJY4T23WKQ3QCWXAYIFGO2Q \
  | 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: e37434e393d6eca86e02b5c18414ced4098b2b1f5675eb9fd87063445e71e92d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4422f1b8142b909679dac91a1c03cd7988b126ac287e305831eda5e2023e98d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-07-28T14:03:36Z",
    "title_canon_sha256": "f034be0ca92add9fdceb0e49278377122445dd910c8b3e4aa6f196c82f524707"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.25738",
    "kind": "arxiv",
    "version": 1
  }
}