Pith Number

pith:EQTO63CU

pith:2004:EQTO63CUK3SX6YJIPOVX6NLDHO

not attested not anchored not stored refs pending

Analysis of Invariants Associated with Spectral Boundary Problems for an Elliptic Operator

Gerd Grubb

arxiv:math/0406145 v1 · 2004-06-08 · math.AP · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EQTO63CUK3SX6YJIPOVX6NLDHO}

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	2026-07-04T14:38:41.727433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2426ef6c5456e57f61287bab7f35633ba173c3a13666b6d770a94d6154115a29

Aliases

arxiv: math/0406145 · arxiv_version: math/0406145v1 · doi: 10.48550/arxiv.math/0406145 · pith_short_12: EQTO63CUK3SX · pith_short_16: EQTO63CUK3SX6YJI · pith_short_8: EQTO63CU

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/EQTO63CUK3SX6YJIPOVX6NLDHO \
  | 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: 2426ef6c5456e57f61287bab7f35633ba173c3a13666b6d770a94d6154115a29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4e980ebd37936fd1f888344a1de45f9e4f957a626ea4fc5e80e83a266af824f",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2004-06-08T15:02:58Z",
    "title_canon_sha256": "e31490449dbb962d2d15017ecece80eb83dd8cd97d01e825d959e9f4195989d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406145",
    "kind": "arxiv",
    "version": 1
  }
}