Pith Number

pith:DA632CPA

pith:2025:DA632CPAWTQS7VBDHZNKC46XCI

not attested not anchored not stored refs pending

Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field

Jukka Tulkki, Mikko Partanen

arxiv:2506.22057 v1 · 2025-06-27 · quant-ph · gr-qc · physics.atom-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DA632CPAWTQS7VBDHZNKC46XCI}

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

1 paper in Pith

Extending unified gravity to account for graviton-graviton interaction

Receipt and verification

First computed	2026-07-05T11:28:21.281338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

183dbd09e0b4e12fd4233e5aa173d7121ba0ce74cff74952dcf20e8c54e4e97c

Aliases

arxiv: 2506.22057 · arxiv_version: 2506.22057v1 · doi: 10.48550/arxiv.2506.22057 · pith_short_12: DA632CPAWTQS · pith_short_16: DA632CPAWTQS7VBD · pith_short_8: DA632CPA

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/DA632CPAWTQS7VBDHZNKC46XCI \
  | 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: 183dbd09e0b4e12fd4233e5aa173d7121ba0ce74cff74952dcf20e8c54e4e97c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27c114a483e78a0c5ec3c27f66f44c82143720da5db2eb8804d5acbef70d657a",
    "cross_cats_sorted": [
      "gr-qc",
      "physics.atom-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-06-27T09:53:35Z",
    "title_canon_sha256": "bc1001917a30e22ea428f7008a3ebef7d26745d130a1659acf266cbbbbbd8b19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.22057",
    "kind": "arxiv",
    "version": 1
  }
}