Pith Number

pith:4ELBZH7N

pith:2005:4ELBZH7NWO5XEGIMUWYL5VP22R

not attested not anchored not stored refs pending

A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices

Steve Fisk

arxiv:math/0502408 v1 · 2005-02-18 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ELBZH7NWO5XEGIMUWYL5VP22R}

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	2026-07-04T14:39:37.653006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1161c9fedb3bb72190ca5b0bed5fad477a1ca864cb34eba9dc2aec9378cf763

Aliases

arxiv: math/0502408 · arxiv_version: math/0502408v1 · doi: 10.48550/arxiv.math/0502408 · pith_short_12: 4ELBZH7NWO5X · pith_short_16: 4ELBZH7NWO5XEGIM · pith_short_8: 4ELBZH7N

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/4ELBZH7NWO5XEGIMUWYL5VP22R \
  | 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: e1161c9fedb3bb72190ca5b0bed5fad477a1ca864cb34eba9dc2aec9378cf763

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbc783db6e4693e89c3d7de703a9c6f0fff1ef50066163b26bf718fd966909fa",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2005-02-18T21:04:02Z",
    "title_canon_sha256": "a2516d2dc38f342c561232ccdb7704d65c41152693e8d598ced1ed771a4b12b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0502408",
    "kind": "arxiv",
    "version": 1
  }
}