Pith Number

pith:XZ7G6RDG

pith:2015:XZ7G6RDGMG3CASHNVMOML5BH5K

not attested not anchored not stored refs pending

Spectral Estimates, Contractions and Hypercontractivity

Emanuel Milman

arxiv:1508.00606 v4 · 2015-08-03 · math.SP · math.DG · 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{XZ7G6RDGMG3CASHNVMOML5BH5K}

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	2026-05-18T00:16:51.014719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be7e6f446661b62048edab1cc5f427eabac548f54cc4226e5b47e9699b1406a8

Aliases

arxiv: 1508.00606 · arxiv_version: 1508.00606v4 · doi: 10.48550/arxiv.1508.00606 · pith_short_12: XZ7G6RDGMG3C · pith_short_16: XZ7G6RDGMG3CASHN · pith_short_8: XZ7G6RDG

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/XZ7G6RDGMG3CASHNVMOML5BH5K \
  | 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: be7e6f446661b62048edab1cc5f427eabac548f54cc4226e5b47e9699b1406a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ecb1955cc837475f208b99417d85050d42a14e08839dda96986584a3ffd04df",
    "cross_cats_sorted": [
      "math.DG",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-08-03T21:37:08Z",
    "title_canon_sha256": "1946e1baa9aac9e963472319ee8f5dab787c8576c1ed583878df667ef99f0783"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.00606",
    "kind": "arxiv",
    "version": 4
  }
}