Pith Number

pith:EY3Y7XNY

pith:2026:EY3Y7XNYE4UL5B2CVNXGKD4JFI

not attested not anchored not stored refs pending

Shape optimisation for adaptive $r$-refinement: the one-dimensional case with residual based error estimators

Philip J. Herbert

arxiv:2607.22206 v1 · 2026-07-24 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EY3Y7XNYE4UL5B2CVNXGKD4JFI}

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	2026-07-27T01:20:53.810135Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26378fddb82728be8742ab6e650f892a12f1dce338a38936659a212bf935a342

Aliases

arxiv: 2607.22206 · arxiv_version: 2607.22206v1 · doi: 10.48550/arxiv.2607.22206 · pith_short_12: EY3Y7XNYE4UL · pith_short_16: EY3Y7XNYE4UL5B2C · pith_short_8: EY3Y7XNY

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/EY3Y7XNYE4UL5B2CVNXGKD4JFI \
  | 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: 26378fddb82728be8742ab6e650f892a12f1dce338a38936659a212bf935a342

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aef1408ba064640988c575acb02c602750a37889fc8d66cdcde626be78dbb5b9",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-07-24T11:22:36Z",
    "title_canon_sha256": "18d35a51a56cf63c0a2e4e6d6e615bfb66398d27718e7dc4d4b723b94e36b28b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.22206",
    "kind": "arxiv",
    "version": 1
  }
}