Pith Number

pith:CZE6RB6N

pith:2007:CZE6RB6NMRWQNZF4LWOTELXTJZ

not attested not anchored not stored refs pending

Non-Metric Gravity II: Spherically Symmetric Solution, Missing Mass and Redshifts of Quasars

Kirill Krasnov, Yuri Shtanov

arxiv:0705.2047 v2 · 2007-05-14 · gr-qc · astro-ph · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CZE6RB6NMRWQNZF4LWOTELXTJZ}

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

A polynomial affine model of gravity: after ten years

Receipt and verification

First computed	2026-07-04T15:24:13.030776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1649e887cd646d06e4bc5d9d322ef34e715492806b51835eac17f8a3abb02514

Aliases

arxiv: 0705.2047 · arxiv_version: 0705.2047v2 · doi: 10.48550/arxiv.0705.2047 · pith_short_12: CZE6RB6NMRWQ · pith_short_16: CZE6RB6NMRWQNZF4 · pith_short_8: CZE6RB6N

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/CZE6RB6NMRWQNZF4LWOTELXTJZ \
  | 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: 1649e887cd646d06e4bc5d9d322ef34e715492806b51835eac17f8a3abb02514

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54c042a2da753ec08a024dd769f01c2c209a57bc62d0df73becb9e89d32d0d1b",
    "cross_cats_sorted": [
      "astro-ph",
      "hep-th"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2007-05-14T22:55:46Z",
    "title_canon_sha256": "4c06bfc1b38878df96a5a0f438486903d2b1a7a9a4d396c952acbc9af579e527"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0705.2047",
    "kind": "arxiv",
    "version": 2
  }
}