Pith Number

pith:OBHUTNAA

pith:2015:OBHUTNAACNRKP7ZQWWUUEOXNPA

not attested not anchored not stored refs pending

Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues

Alex Barnett, Andrew Hassell, Melissa Tacy

arxiv:1512.04165 v2 · 2015-12-14 · math.AP · math.NA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OBHUTNAACNRKP7ZQWWUUEOXNPA}

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	2026-05-18T00:00:46.049082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

704f49b4001362a7ff30b5a9423aed782442a3f2dd886c1b99ff9928a1b6e4c4

Aliases

arxiv: 1512.04165 · arxiv_version: 1512.04165v2 · doi: 10.48550/arxiv.1512.04165 · pith_short_12: OBHUTNAACNRK · pith_short_16: OBHUTNAACNRKP7ZQ · pith_short_8: OBHUTNAA

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/OBHUTNAACNRKP7ZQWWUUEOXNPA \
  | 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: 704f49b4001362a7ff30b5a9423aed782442a3f2dd886c1b99ff9928a1b6e4c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80de2e422923fbc2e88b3ea3b09cd39df7af5c489951c9409da52eada41e5cc5",
    "cross_cats_sorted": [
      "math.NA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-12-14T04:17:38Z",
    "title_canon_sha256": "30b3c30a4736ed359110423d01f251fcad4d4f389e7e39ce898f4a3a101b28b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04165",
    "kind": "arxiv",
    "version": 2
  }
}