Pith Number

pith:PDL5334W

pith:2024:PDL5334WIN32WNBCCTQKWE2ZUT

not attested not anchored not stored refs resolved

On R-trees, homotopies, and covering maps

Curtis Kent, Gregory R. Conner, Jeremy Brazas, Paul Fabel

Every map of manifolds with the unique path lifting property is a covering map

arxiv:2401.08883 v2 · 2024-01-16 · math.AT · math.GN · math.GT

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\pithnumber{PDL5334WIN32WNBCCTQKWE2ZUT}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

every map of manifolds with the unique path lifting property is a covering map

C2weakest assumption

The equivalence relation of homotopies of paths rel. endpoints is generated by inserting and deleting one-dimensional backtracking (abstract).

C3one line summary

Quotients of R-trees under group actions with unique path lifting contain no discs, implying that maps of manifolds with unique path lifting are covering maps, via the result that path homotopies are generated by one-dimensional backtracking.

References

20 extracted · 20 resolved · 1 Pith anchors

[1] R.C. Alperin, K.N. Moss, Complete trees for groups with a real-valued length function, J. London Math. Soc. 31 (1985) no. 2, 55-68 1985

[2] R. D. Anderson, A continuous curve admitting monotone open maps onto all locally connected metric continua, BAMS 62 (1956) 264-265 1956

[3] Berestovski i , C.P 2007

[4] Berestovski i , C.P 2010

[5] Bestvina, -trees in topology, geometry and group theory, Handbook of Geometric Topology, edited by R 2002

Receipt and verification

First computed	2026-05-27T14:06:35.317904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78d7ddef964377ab342214e0ab1359a4d306f586b0257ad953fcf233058b3972

Aliases

arxiv: 2401.08883 · arxiv_version: 2401.08883v2 · doi: 10.48550/arxiv.2401.08883 · pith_short_12: PDL5334WIN32 · pith_short_16: PDL5334WIN32WNBC · pith_short_8: PDL5334W

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PDL5334WIN32WNBCCTQKWE2ZUT \
  | 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: 78d7ddef964377ab342214e0ab1359a4d306f586b0257ad953fcf233058b3972

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a97e8d341ac6cbc71cdb34939c4213042eca08e624033af347ecd4eb0758a5f",
    "cross_cats_sorted": [
      "math.GN",
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2024-01-16T23:40:39Z",
    "title_canon_sha256": "1a159a79a1097a5753d822ceab42cb46e8fb936049dd9e98b577c50df83a2a26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2401.08883",
    "kind": "arxiv",
    "version": 2
  }
}