Pith Number

pith:Y3KETHWR

pith:2026:Y3KETHWR7UGVLKESKS7VQ4WLCS

not attested not anchored not stored refs resolved

Singular multivalued homology

Alejandro O. Majadas-Moure

Multivalued singular homology vanishes in all positive degrees for compact Hausdorff spaces.

arxiv:2605.12585 v1 · 2026-05-12 · math.AT · math.KT

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\usepackage{pith}
\pithnumber{Y3KETHWR7UGVLKESKS7VQ4WLCS}

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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

Let X be a compact, Hausdorff topological space. Then H^M_n(X)=0 for all n>0, where H_n is the multivalued analogue of singular homology.

C2weakest assumption

The multivalued homology construction is well-defined on compact Hausdorff spaces and the topological properties of compactness and the Hausdorff axiom are sufficient to force vanishing in every positive degree.

C3one line summary

Multivalued singular homology vanishes in all positive degrees for compact Hausdorff spaces.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] Bourbaki (1971) 1971

[2] S. Eilenberg, D. Montgomery (1946).Fixed point theorems for multivalued transfor- mations, Amer. J. Math.58, 214–222 1946

[3] P. G. Goerss, J. F. Jardine (1999).Simplicial homotopy theory, Progress in Mathe- matics,174, 510 pp 1999

[4] Grothendieck et al.,S´ eminaire de G´ eom˜ netrie Alg´ ebrique, SGA5, Lecture Notes in Math.,589, Springer, 1977 1977

[5] Kakutani (1941).A generalization of Brouwer’s fixed point theorem, Duke Mat 1941

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:10:01.362197Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6d4499ed1fd0d55a89254bf5872cb148859ba6b7e982dead8655cc0f2fdf42b

Aliases

arxiv: 2605.12585 · arxiv_version: 2605.12585v1 · doi: 10.48550/arxiv.2605.12585 · pith_short_12: Y3KETHWR7UGV · pith_short_16: Y3KETHWR7UGVLKES · pith_short_8: Y3KETHWR

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/Y3KETHWR7UGVLKESKS7VQ4WLCS \
  | 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: c6d4499ed1fd0d55a89254bf5872cb148859ba6b7e982dead8655cc0f2fdf42b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46e4854a2076244c717911f61f54526c97ea355c1bd66ec2a3a0ba5e4c70f4a5",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-05-12T17:55:26Z",
    "title_canon_sha256": "9e2e904a38315e61c1a0b330f8acb8a2cb28b0a3c689aaecb26e1f47bcc9b2bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12585",
    "kind": "arxiv",
    "version": 1
  }
}