Pith Number

pith:TOWPHGBS

pith:2021:TOWPHGBS6JZYRRO2XUMNQT2CFO

not attested not anchored not stored refs pending

Optimal maps and local-to-global property in negative dimensional spaces with Ricci curvature bounded from below

Chiara Rigoni, Mattia Magnabosco

arxiv:2105.12017 v1 · 2021-05-25 · math.DG · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TOWPHGBS6JZYRRO2XUMNQT2CFO}

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.

Receipt and verification

First computed	2026-07-05T02:42:59.319339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bacf39832f27388c5dabd18d84f422bb3fa3bd28d7b8edc9abcb64e14ddb678

Aliases

arxiv: 2105.12017 · arxiv_version: 2105.12017v1 · doi: 10.48550/arxiv.2105.12017 · pith_short_12: TOWPHGBS6JZY · pith_short_16: TOWPHGBS6JZYRRO2 · pith_short_8: TOWPHGBS

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/TOWPHGBS6JZYRRO2XUMNQT2CFO \
  | 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: 9bacf39832f27388c5dabd18d84f422bb3fa3bd28d7b8edc9abcb64e14ddb678

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31717da1da8de4ed3a755734d7b65220c0800fa3bb5fe86d74ed31d1f020c1d7",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-05-25T15:38:01Z",
    "title_canon_sha256": "6f970ebe53bd4c1fd07ca3720aef8bf534685b1a59b8270169f3caee8f9414f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.12017",
    "kind": "arxiv",
    "version": 1
  }
}