Pith Number

pith:TEIOMHJT

pith:2026:TEIOMHJTIAWZPAC2D57CFCFFGH

not attested not anchored not stored refs resolved

All Circuits Lead to Rome: Rethinking Functional Anisotropy in Circuit and Sheaf Discovery for LLMs

Bangwei Guo, Dimitris N. Metaxas, Gerald Penn, Jingcheng Niu, Jinman Zhao, Mingyu Jin, Xi Chen, Yutao Yue, Yutong Yin, Zhaoran Wang

A single task in large language models can be performed by multiple structurally distinct circuits or sheaves that are all faithful, sparse, and complete.

arxiv:2605.12671 v1 · 2026-05-12 · cs.CL

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\pithnumber{TEIOMHJTIAWZPAC2D57CFCFFGH}

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2 Internet Archive

3 Author claim open · sign in to claim

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 show that a single LLM task can instead be supported by multiple, structurally distinct circuits or sheaves that are simultaneously faithful, sparse, and complete.

C2weakest assumption

That the Overlap-Aware Sheaf Repulsion penalty successfully uncovers genuinely distinct mechanisms without introducing methodological artifacts, and that the theoretical analysis of high-dimensional superposition holds under the stated mild assumptions.

C3one line summary

LLM tasks are supported by multiple distinct circuits rather than unique mechanisms, demonstrated via Overlap-Aware Sheaf Repulsion and the Distributive Dense Circuit Hypothesis.

References

300 extracted · 300 resolved · 5 Pith anchors

[1] Abdelmalik, Philip and Peron, Emilie and Schnitzler, Johannes and Fontaine, Julie and Elfenkampera, Eva and Barbozaa, Philippe , year = 2018, journal = 2018

[2] Proceedings of the 25th

[3] From Language as System to Language as Use:

[4] Ackema, Peter and Neeleman, Ad , year = 2004, publisher = 2004

[5] Adger, David , year = 2003, publisher = 2003

Receipt and verification

First computed	2026-05-18T03:09:50.224482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9910e61d33402d97805a1f7e2288a531ce206f4307ac3f8348a0d04acbd89c17

Aliases

arxiv: 2605.12671 · arxiv_version: 2605.12671v1 · doi: 10.48550/arxiv.2605.12671 · pith_short_12: TEIOMHJTIAWZ · pith_short_16: TEIOMHJTIAWZPAC2 · pith_short_8: TEIOMHJT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TEIOMHJTIAWZPAC2D57CFCFFGH \
  | 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: 9910e61d33402d97805a1f7e2288a531ce206f4307ac3f8348a0d04acbd89c17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b372839d2a82aa15f4353102729121b01c37f1d4d0a56b1c7fe98881c2c3946b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CL",
    "submitted_at": "2026-05-12T19:21:23Z",
    "title_canon_sha256": "aaf33bf90f03f84b493997633b106b7f4a97226a4afbb66ab912e25b746151bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12671",
    "kind": "arxiv",
    "version": 1
  }
}