Pith Number

pith:VZ5UD47Q

pith:2017:VZ5UD47QWHWDW6PCSSMCJANUCR

not attested not anchored not stored refs pending

Interlacing Families III: Sharper Restricted Invertibility Estimates

Adam W. Marcus, Daniel A. Spielman, Nikhil Srivastava

arxiv:1712.07766 v1 · 2017-12-21 · 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{VZ5UD47QWHWDW6PCSSMCJANUCR}

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	2026-05-18T00:27:30.961809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae7b41f3f0b1ec3b79e294982481b4146ce5059d9bcf2b6807abb5d4c7122d5b

Aliases

arxiv: 1712.07766 · arxiv_version: 1712.07766v1 · doi: 10.48550/arxiv.1712.07766 · pith_short_12: VZ5UD47QWHWD · pith_short_16: VZ5UD47QWHWDW6PC · pith_short_8: VZ5UD47Q

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/VZ5UD47QWHWDW6PCSSMCJANUCR \
  | 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: ae7b41f3f0b1ec3b79e294982481b4146ce5059d9bcf2b6807abb5d4c7122d5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf4d2c624421e87bbaf07ae5e2cbb321ccc136d6191e3d71a59b5179638aa6b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-12-21T01:53:11Z",
    "title_canon_sha256": "a5a5d170d871a8077edbc49c0254d2efc91fed04b40126f1c4ca3ff55d0b67af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.07766",
    "kind": "arxiv",
    "version": 1
  }
}