Pith Number

pith:VVTK3ZUW

pith:2025:VVTK3ZUWDD44DK62PRKACIILRY

not attested not anchored not stored refs pending

Structure of Metric $1$-currents: approximation by normal currents and representation results

David Bate, Emanuele Caputo, Jakub Tak\'a\v{c}, Phoebe Valentine, Pietro Wald

arxiv:2508.08017 v1 · 2025-08-11 · math.MG · math.AP · math.FA

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VVTK3ZUWDD44DK62PRKACIILRY}

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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.

Cited by

1 paper in Pith

Lipschitz-free spaces and purely 1-unrectifiable metric spaces

Receipt and verification

First computed	2026-07-05T11:52:06.531408Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad66ade69618f9c1abda7c5401210b8e2759958868b7813ae0fa0dc175d39ba2

Aliases

arxiv: 2508.08017 · arxiv_version: 2508.08017v1 · doi: 10.48550/arxiv.2508.08017 · pith_short_12: VVTK3ZUWDD44 · pith_short_16: VVTK3ZUWDD44DK62 · pith_short_8: VVTK3ZUW

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/VVTK3ZUWDD44DK62PRKACIILRY \
  | 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: ad66ade69618f9c1abda7c5401210b8e2759958868b7813ae0fa0dc175d39ba2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ffd641e776efee854425d04cdffafdb10c2f243cf022ce605ed6c4771790c424",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2025-08-11T14:25:12Z",
    "title_canon_sha256": "fbc6f8fd91b2fe3baff788ce22eee9a1a1d883511adc8cf4e41832146316bc36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.08017",
    "kind": "arxiv",
    "version": 1
  }
}