Pith Number

pith:CGPFGPG4

pith:2010:CGPFGPG4BOH7PJKIOGU2WTHTH5

not attested not anchored not stored refs pending

Alternatives to dark matter: Modified gravity as an alternative to dark matter

Jacob D. Bekenstein

arxiv:1001.3876 v1 · 2010-01-21 · astro-ph.CO · gr-qc · 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{CGPFGPG4BOH7PJKIOGU2WTHTH5}

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	2026-07-04T17:20:07.943196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

119e533cdc0b8ff7a54871a9ab4cf33f59600d17c7b206551d411a0b3df53e64

Aliases

arxiv: 1001.3876 · arxiv_version: 1001.3876v1 · doi: 10.48550/arxiv.1001.3876 · pith_short_12: CGPFGPG4BOH7 · pith_short_16: CGPFGPG4BOH7PJKI · pith_short_8: CGPFGPG4

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/CGPFGPG4BOH7PJKIOGU2WTHTH5 \
  | 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: 119e533cdc0b8ff7a54871a9ab4cf33f59600d17c7b206551d411a0b3df53e64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55a991bba7dfaff4f0ef48539724cb8b3006090949721420bfe18263c24acce0",
    "cross_cats_sorted": [
      "gr-qc",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2010-01-21T21:01:03Z",
    "title_canon_sha256": "aaa165e13a488fbe64c5c4807ac04edf67ff71eba5bdcc5c353da98dd32b6e2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.3876",
    "kind": "arxiv",
    "version": 1
  }
}