Pith Number

pith:NIHXPCUZ

pith:2015:NIHXPCUZBUKARCQSC74PFMGATU

not attested not anchored not stored refs pending

Optimal Neumann control for the 1D wave equation: finite horizon, infinite horizon, boundary tracking terms and the turnpike property

Emmanuel Tr\'elat (LJLL), Enrique Zuazua (BCAM), Martin Gugat

arxiv:1505.05017 v1 · 2015-05-19 · 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{NIHXPCUZBUKARCQSC74PFMGATU}

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	2026-05-18T02:05:22.482725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a0f778a990d14088a1217f8f2b0c09d1ca8249420d205eb57647a92332bc48d

Aliases

arxiv: 1505.05017 · arxiv_version: 1505.05017v1 · doi: 10.48550/arxiv.1505.05017 · pith_short_12: NIHXPCUZBUKA · pith_short_16: NIHXPCUZBUKARCQS · pith_short_8: NIHXPCUZ

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/NIHXPCUZBUKARCQSC74PFMGATU \
  | 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: 6a0f778a990d14088a1217f8f2b0c09d1ca8249420d205eb57647a92332bc48d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5eadee5f1579444938fabf6e702bf2fa046d1502820baff7190f78321ba0768e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-05-19T14:31:44Z",
    "title_canon_sha256": "3834aab085094baee8880b26c7eecf7d127ce9a752f4fad2c8f50efa71331503"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.05017",
    "kind": "arxiv",
    "version": 1
  }
}