Pith Number

pith:BLF7CIBQ

pith:2026:BLF7CIBQLN4C2LVLL4RPNDRTKU

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The Emergence of Measured Geometry in Self-Gravitating Systems

Francisco S. N. Lobo, Julian Barbour, Maria I. R. Louren\c{c}o

Systematic radial variations in nearest-neighbor separations indicate that geometry in self-gravitating N-body systems emerges from gravitational interactions.

arxiv:2602.18115 v2 · 2026-02-20 · gr-qc · physics.hist-ph

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\pithnumber{BLF7CIBQLN4C2LVLL4RPNDRTKU}

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Record completeness

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4 Citations open

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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

We argue that these variations reflect a context-dependent, emergent effective geometry shaped by gravitational interactions, in accordance with Poincaré's assertion that measured geometry depends on the forces influencing measuring devices, and Einstein's view that rods and clocks define physical geometry through their local dynamics.

C2weakest assumption

That systematic variations in nearest-neighbor separations observed in central configurations constitute direct evidence for an emergent, context-dependent measured geometry in the operational sense of Poincaré and Einstein, rather than arising as a kinematic consequence of the equilibrium condition itself.

C3one line summary

Numerical analysis of central configurations reveals radial variations in nearest-neighbor distances, interpreted as evidence that measured geometry in self-gravitating Newtonian systems emerges from gravitational interactions rather than serving as a fixed background.

Receipt and verification

First computed	2026-05-17T23:39:16.047595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0acbf120305b782d2eab5f22f68e33552ac1e46ef16b16850626b00b0e191b2f

Aliases

arxiv: 2602.18115 · arxiv_version: 2602.18115v2 · doi: 10.48550/arxiv.2602.18115 · pith_short_12: BLF7CIBQLN4C · pith_short_16: BLF7CIBQLN4C2LVL · pith_short_8: BLF7CIBQ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BLF7CIBQLN4C2LVLL4RPNDRTKU \
  | 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: 0acbf120305b782d2eab5f22f68e33552ac1e46ef16b16850626b00b0e191b2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3d09e487bc686c98a21ec20e567a6d70c73cbc129ba6334d5f818d9181d461a",
    "cross_cats_sorted": [
      "physics.hist-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-02-20T10:07:42Z",
    "title_canon_sha256": "66afbda61079a22a1748ff3688c14d4dde2e5eb312b03a81a45a5dc71455cbcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.18115",
    "kind": "arxiv",
    "version": 2
  }
}