Pith Number

pith:IZ3XSSGK

pith:2015:IZ3XSSGKVUPZCOPR63SE6VCOXN

not attested not anchored not stored refs pending

Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues

Alfred Wagner, Catherine Bandle

arxiv:1512.04699 v1 · 2015-12-15 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IZ3XSSGKVUPZCOPR63SE6VCOXN}

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	2026-05-18T01:24:19.639849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46777948caad1f9139f1f6e44f544ebb4c5f73af3dc481fbaf669885bc90bdb3

Aliases

arxiv: 1512.04699 · arxiv_version: 1512.04699v1 · doi: 10.48550/arxiv.1512.04699 · pith_short_12: IZ3XSSGKVUPZ · pith_short_16: IZ3XSSGKVUPZCOPR · pith_short_8: IZ3XSSGK

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/IZ3XSSGKVUPZCOPR63SE6VCOXN \
  | 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: 46777948caad1f9139f1f6e44f544ebb4c5f73af3dc481fbaf669885bc90bdb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "779c679e994b9c3260f59ab376be3e91f63c79447230593c1d58a8c2153b2df6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-12-15T09:51:49Z",
    "title_canon_sha256": "0d12cf96c529354a6f361b5e9d3278b597e2497d2fe26ba92fe64a2a213e0366"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04699",
    "kind": "arxiv",
    "version": 1
  }
}