Pith Number

pith:VNWTJR3M

pith:2026:VNWTJR3MCXLUVTYZ36I4N4NX6K

not attested not anchored not stored refs resolved

Intrinsic uniform structure on median algebras

Michael Megrelishvili

Median algebras carry an intrinsic uniformity whose completion is the minimal median compactification coinciding with the Roller compactification for finite intervals.

arxiv:2605.16096 v1 · 2026-05-15 · math.GN · math.DS · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VNWTJR3MCXLUVTYZ36I4N4NX6K}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

In the finite-rank case, the resulting compact G-system is Rosenthal representable and hence dynamically tame.

C2weakest assumption

The assumption that all intervals in the median algebra X are finite (or that the algebra has finite rank), which is invoked to conclude uniqueness of the MMC as a proper median compactification and its coincidence with the Roller compactification, as well as the Rosenthal representability of the G-system.

C3one line summary

Defines the median uniformity U_m on median algebras to construct the Minimal Median Compactification (MMC) as a natural compactification for group actions by median automorphisms, with uniqueness and tameness results under finite intervals or finite rank.

References

24 extracted · 24 resolved · 3 Pith anchors

[1] Bowditch,Treelike structures arising from continua and convergence groups, Mem 1999

[2] Bowditch,Embedding median algebras in products of trees, Geometriae Dedicata170(2014), 157–176 2014

[3] Bowditch,Median Algebras, Preprint (2024) 2024

[4] I. Chatterji, C. Drutu, F. Haglund,Kazhdan and Haagerup properties from the median viewpoint, Adv. Math. 225(2010) 882–921 2010

[5] M. Couceiro, J.L. Marichal, B. TeheuxConservative Median Algebras and Semilattices, Order,33(2016), 121–132 2016

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:52.432274Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab6d34c76c15d74acf19df91c6f1b7f2bb3d76d89f1e0a775d2179993efa53a4

Aliases

arxiv: 2605.16096 · arxiv_version: 2605.16096v1 · doi: 10.48550/arxiv.2605.16096 · pith_short_12: VNWTJR3MCXLU · pith_short_16: VNWTJR3MCXLUVTYZ · pith_short_8: VNWTJR3M

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/VNWTJR3MCXLUVTYZ36I4N4NX6K \
  | 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: ab6d34c76c15d74acf19df91c6f1b7f2bb3d76d89f1e0a775d2179993efa53a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e4ffe504fde871aa4964b3997f554f13e7b78d0bebbee3be8bc8301be6d3e21",
    "cross_cats_sorted": [
      "math.DS",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2026-05-15T15:51:21Z",
    "title_canon_sha256": "904f41ee95733b8065e97b9fe3f3c97c29a0fd7b7cb0f4c2d4973bebd6fbdb81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16096",
    "kind": "arxiv",
    "version": 1
  }
}