Pith Number

pith:XJ2KP6WG

pith:2016:XJ2KP6WGWUROANNX5T7X3OVXOR

not attested not anchored not stored refs pending

Principal submatrices, restricted invertibility and a quantitative Gauss-Lucas theorem

Mohan Ravichandran

arxiv:1609.04187 v2 · 2016-09-14 · math.FA · math.CO · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XJ2KP6WGWUROANNX5T7X3OVXOR}

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	2026-05-18T00:48:42.391278Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba74a7fac6b522e035b7ecff7dbab774674e3d7c0a038e7da6332ebf15a43f03

Aliases

arxiv: 1609.04187 · arxiv_version: 1609.04187v2 · doi: 10.48550/arxiv.1609.04187 · pith_short_12: XJ2KP6WGWURO · pith_short_16: XJ2KP6WGWUROANNX · pith_short_8: XJ2KP6WG

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/XJ2KP6WGWUROANNX5T7X3OVXOR \
  | 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: ba74a7fac6b522e035b7ecff7dbab774674e3d7c0a038e7da6332ebf15a43f03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bb12d6e5e4260b889b411908043c1b4b80ced03225e6a12b88d80f9302c9b8e",
    "cross_cats_sorted": [
      "math.CO",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-09-14T09:31:54Z",
    "title_canon_sha256": "fd61854bd5af34008d394af11322e69ace11f886c65ef310f01aef6d89f0a78d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.04187",
    "kind": "arxiv",
    "version": 2
  }
}