Pith Number

pith:JD2XRVHC

pith:2026:JD2XRVHCZAXXJ2EBZXAOOSXQNH

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Geodesic currents of coarse negative curvature

D\'idac Mart\'inez-Granado, Meenakshy Jyothis

Geodesic currents with strongly hyperbolic dual pseudometrics are dense in the full space of currents.

arxiv:2605.14469 v1 · 2026-05-14 · math.GT

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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 prove that the subset of geodesic currents whose dual pseudometric is strongly hyperbolic is dense in the space of geodesic currents.

C2weakest assumption

The characterization of strong hyperbolicity in terms of boundary data for pseudometrics dual to geodesic currents is valid and the elementary finite-cover argument applies without further restrictions on the surface or the currents.

C3one line summary

Strongly hyperbolic geodesic currents are dense in the space of geodesic currents, yielding infinitely many pairwise non-roughly-isometric strongly hyperbolic metrics on the universal cover that are not CAT(0).

References

58 extracted · 58 resolved · 3 Pith anchors

[1] The pressure metric for Anosov representations 2015 · arXiv:1301.7459

[2] Bridson and Andre Haefliger, Metric spaces of nonpositive curvature, Springer, 2011 2011

[3] M. Burger, A. Iozzi, A. Parreau, and M. B. Pozzetti, Currents, systoles, and compactifications of character varieties, Proc. Lond. Math. Soc. (3) 123 (2021), no. 6, 565--596 2021

[4] Marc Burger, Alessandra Iozzi, Anne Parreau, and Maria Beatrice Pozzetti, Positive crossratios, barycenters, trees and applications to maximal representations, 2021 2021

[5] Systems 18 (1998), no 1998

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:06.684175Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48f578d4e2c82f74e881cdc0e74af069ec0acf609d87121716eed7ad792e6e95

Aliases

arxiv: 2605.14469 · arxiv_version: 2605.14469v1 · doi: 10.48550/arxiv.2605.14469 · pith_short_12: JD2XRVHCZAXX · pith_short_16: JD2XRVHCZAXXJ2EB · pith_short_8: JD2XRVHC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JD2XRVHCZAXXJ2EBZXAOOSXQNH \
  | 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: 48f578d4e2c82f74e881cdc0e74af069ec0acf609d87121716eed7ad792e6e95

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c76267596403dc6f2f67ea5087ac90d2ea0f0187c03bbe0f88d9875b9499c87",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-14T07:04:20Z",
    "title_canon_sha256": "84a96322c296535e67cd7c61209aac637c629c7cec433edfafb73474f7b07ec6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14469",
    "kind": "arxiv",
    "version": 1
  }
}