Pith Number

pith:6O2HXGFE

pith:2026:6O2HXGFETSGQRUAOIOVLMTQTQV

not attested not anchored not stored refs pending

Linear-size $\ell_1$ sparsifiers

Thomas Rothvoss, Victor Reis

arxiv:2606.28147 v1 · 2026-06-26 · math.MG · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6O2HXGFETSGQRUAOIOVLMTQTQV}

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	2026-06-29T01:15:07.393195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3b47b98a49c8d08d00e43aab64e1385625842c94bb070ea0cc6a49ee0e17453

Aliases

arxiv: 2606.28147 · arxiv_version: 2606.28147v1 · doi: 10.48550/arxiv.2606.28147 · pith_short_12: 6O2HXGFETSGQ · pith_short_16: 6O2HXGFETSGQRUAO · pith_short_8: 6O2HXGFE

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/6O2HXGFETSGQRUAOIOVLMTQTQV \
  | 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: f3b47b98a49c8d08d00e43aab64e1385625842c94bb070ea0cc6a49ee0e17453

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07deee118cbfd06b9977779f492340e9b04c4971ff3e041a0b9ca99a0f0f60fc",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2026-06-26T14:43:15Z",
    "title_canon_sha256": "c812c402d70e00475c7809a9e2faa791330b632735a6958b50fafc0625b478de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.28147",
    "kind": "arxiv",
    "version": 1
  }
}