Pith Number

pith:45QYTIVE

pith:2013:45QYTIVEU6NEM4CZRFEMMJ4Y6U

not attested not anchored not stored refs pending

On eigenfunction expansions of first-order symmetric systems and ordinary differential operators of an odd order

Vadim Mogilevskii

arxiv:1307.6741 v1 · 2013-07-25 · 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{45QYTIVEU6NEM4CZRFEMMJ4Y6U}

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	2026-05-18T03:17:34.809540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e76189a2a4a79a4670598948c62798f52410815c563f2b68d2301359b62d236e

Aliases

arxiv: 1307.6741 · arxiv_version: 1307.6741v1 · doi: 10.48550/arxiv.1307.6741 · pith_short_12: 45QYTIVEU6NE · pith_short_16: 45QYTIVEU6NEM4CZ · pith_short_8: 45QYTIVE

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/45QYTIVEU6NEM4CZRFEMMJ4Y6U \
  | 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: e76189a2a4a79a4670598948c62798f52410815c563f2b68d2301359b62d236e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af800c2c811428d649b32312ee5b4c34529994998735da89e9ea332937a29dbd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-07-25T13:43:14Z",
    "title_canon_sha256": "726e0a3462ddcab6bd5a72b354fa04bb7de2091124aa48489538a504cf021f39"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.6741",
    "kind": "arxiv",
    "version": 1
  }
}