Pith Number

pith:66P2W5RZ

pith:2026:66P2W5RZE2M6ME4TSOBPOTAP7M

not attested not anchored not stored refs pending

R$^3$L: Reasoning 3D Layouts from Relative Spatial Relations

Bing Wang, Yuqi Wang, Zhifeng Gu

Decomposing spatial relations into invariant parts and adding an imagine-and-revise loop produces more consistent 3D layouts from relative instructions.

arxiv:2605.06758 v2 · 2026-05-07 · cs.CV · cs.AI · cs.LG · cs.RO

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\usepackage{pith}
\pithnumber{66P2W5RZE2M6ME4TSOBPOTAP7M}

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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

R³L produces more physically feasible and semantically consistent layouts; resolving frame-induced inconsistencies is crucial for reliable multi-hop relative spatial reasoning.

C2weakest assumption

That the proposed invariant decomposition and imagine-and-revise loop actually eliminate the dominant sources of semantic and metric drift without introducing new inconsistencies or losing necessary spatial information.

C3one line summary

R³L improves reliability of 3D layout generation from relative spatial relations by breaking error-accumulating chains with decomposition and enforcing self-consistency via imagination and revision.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T01:06:09.850717Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f79fab76392699e613939382f74c0ffb30419e253930989b68750353fc8c5404

Aliases

arxiv: 2605.06758 · arxiv_version: 2605.06758v2 · doi: 10.48550/arxiv.2605.06758 · pith_short_12: 66P2W5RZE2M6 · pith_short_16: 66P2W5RZE2M6ME4T · pith_short_8: 66P2W5RZ

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/66P2W5RZE2M6ME4TSOBPOTAP7M \
  | 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: f79fab76392699e613939382f74c0ffb30419e253930989b68750353fc8c5404

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d6fb122c751fa8ca76605d828b88669473426aa5b3d0699ccc1ad1c36f63f59",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG",
      "cs.RO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CV",
    "submitted_at": "2026-05-07T16:50:12Z",
    "title_canon_sha256": "455caca4da9aad458046cf15a5f02a5360b59f917ece4f22288116c1decc3377"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.06758",
    "kind": "arxiv",
    "version": 2
  }
}