Pith Number

pith:O4WTURIW

pith:2026:O4WTURIWU4CGGUJQ7ZZRP43ASG

not attested not anchored not stored refs pending

On the sharpness of the $C^1$-norm threshold for perturbations in the normally hyperbolic invariant manifold theorem---a toy model perspective

Junhao Li, Lin Wang, Yujie Huang

arxiv:2608.04862 v1 · 2026-08-05 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O4WTURIWU4CGGUJQ7ZZRP43ASG}

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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	2026-08-06T01:47:25.155585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

772d3a4516a704635130fe7317f36091a80e11c70f901a908df3fcbf1d4a2fec

Aliases

arxiv: 2608.04862 · arxiv_version: 2608.04862v1 · doi: 10.48550/arxiv.2608.04862 · pith_short_12: O4WTURIWU4CG · pith_short_16: O4WTURIWU4CGGUJQ · pith_short_8: O4WTURIW

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/O4WTURIWU4CGGUJQ7ZZRP43ASG \
  | 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: 772d3a4516a704635130fe7317f36091a80e11c70f901a908df3fcbf1d4a2fec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea28cc473b3d24948197540e7a5846da5b37c141f29bb70c7ea0e160afe7e062",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-08-05T13:54:33Z",
    "title_canon_sha256": "6008931a3f34664adecf67b24456057c38846b4290cac5458a1863d4803d0fde"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04862",
    "kind": "arxiv",
    "version": 1
  }
}