Pith Number

pith:TBMITQLQ

pith:2026:TBMITQLQKXF2FXGDXFWV5AH76A

not attested not anchored not stored refs pending

Modified Mukhanov-Sasaki equation and primordial perturbations in $\kappa$-deformed non-commutative space-time

Puxun Wu, Vishnu Rajagopal, Yang Lei

arxiv:2607.24277 v1 · 2026-07-27 · 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{TBMITQLQKXF2FXGDXFWV5AH76A}

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	2026-07-28T02:23:54.873599Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

985889c17055cba2dcc3b96d5e80fff02551108fac5bc1efdcf64486b79c9661

Aliases

arxiv: 2607.24277 · arxiv_version: 2607.24277v1 · doi: 10.48550/arxiv.2607.24277 · pith_short_12: TBMITQLQKXF2 · pith_short_16: TBMITQLQKXF2FXGD · pith_short_8: TBMITQLQ

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/TBMITQLQKXF2FXGDXFWV5AH76A \
  | 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: 985889c17055cba2dcc3b96d5e80fff02551108fac5bc1efdcf64486b79c9661

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd3664b9f43567fbad9a254449cbe3673006559af0a247b27c6217d1acf6f47e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-07-27T11:24:07Z",
    "title_canon_sha256": "92702db4e10389906ffd467cabca12390aedfc8a7bb62840408f0e56f8fe1845"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24277",
    "kind": "arxiv",
    "version": 1
  }
}