Pith Number

pith:EYBZWPA4

pith:2015:EYBZWPA4PUP4GQG5RQL2RO5KUA

not attested not anchored not stored refs pending

Useful bounds on the extreme eigenvalues and vectors of matrices for Harper's operators

Angela Hicks, Daniel Bump, Harold Widom, Laurent Miclo, Persi Diaconis

arxiv:1508.05986 v2 · 2015-08-24 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EYBZWPA4PUP4GQG5RQL2RO5KUA}

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	2026-05-18T01:27:31.282134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26039b3c1c7d1fc340dd8c17a8bbaaa016f4d958f224e488e7c9bd2814883dfb

Aliases

arxiv: 1508.05986 · arxiv_version: 1508.05986v2 · doi: 10.48550/arxiv.1508.05986 · pith_short_12: EYBZWPA4PUP4 · pith_short_16: EYBZWPA4PUP4GQG5 · pith_short_8: EYBZWPA4

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/EYBZWPA4PUP4GQG5RQL2RO5KUA \
  | 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: 26039b3c1c7d1fc340dd8c17a8bbaaa016f4d958f224e488e7c9bd2814883dfb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f47fb73a9dbea421820889c2c5ab95839841e4748d14c9dfb765331c5dee7a94",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-08-24T22:25:27Z",
    "title_canon_sha256": "2cdc1128e4574b0b9c1a31d22a21d95600c78e51cdf26f21f0ee91d249c616a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05986",
    "kind": "arxiv",
    "version": 2
  }
}