Pith Number

pith:XIVE3P7D

pith:2026:XIVE3P7DBD7OIO4FXZKDCR6K4R

not attested not anchored not stored refs pending

On the residual missing mass of the Bullet Cluster

Benoit Famaey

The Bullet Cluster exhibits the same residual missing mass discrepancy under MOND as other similar-mass clusters, with the missing mass being collisionless and centered on galaxies.

arxiv:2605.10022 v2 · 2026-05-11 · astro-ph.CO · gr-qc

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\usepackage{pith}
\pithnumber{XIVE3P7DBD7OIO4FXZKDCR6K4R}

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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.

Claims

C1strongest claim

I confirm here that this cluster exhibits the same residual missing mass discrepancy as other clusters of similar mass in the MOND context. Moreover, this missing mass should be mostly collisionless, since it is centred on the galaxies of the Bullet Cluster.

C2weakest assumption

The updated JWST-based gravitational lens model correctly captures the total mass distribution without significant systematic errors, and the MOND calculation for the expected baryonic contribution is accurate for this system.

C3one line summary

The Bullet Cluster exhibits a residual missing mass in MOND that is collisionless and galaxy-centered, matching other clusters of similar mass.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:35.359514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba2a4dbfe308fee43b85be543147cae469f4d1012160b104dde6347635503f5f

Aliases

arxiv: 2605.10022 · arxiv_version: 2605.10022v2 · doi: 10.48550/arxiv.2605.10022 · pith_short_12: XIVE3P7DBD7O · pith_short_16: XIVE3P7DBD7OIO4F · pith_short_8: XIVE3P7D

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/XIVE3P7DBD7OIO4FXZKDCR6K4R \
  | 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: ba2a4dbfe308fee43b85be543147cae469f4d1012160b104dde6347635503f5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1c257e353e14b614cd73b5d4f6bdb0b50633a09eae33e9561bcf18f5e38cc07",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2026-05-11T05:45:56Z",
    "title_canon_sha256": "2517959b20f8aededfc4cba3a4868c20ec98dc41661a179e76b13df6307b90cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10022",
    "kind": "arxiv",
    "version": 2
  }
}