Pith Number

pith:MIT32RYL

pith:2015:MIT32RYLJWJFNZTFHZ4JCQ2F4R

not attested not anchored not stored refs pending

Spectral Invariance of Non-Smooth Pseudodifferential Operators

Christine Pfeuffer, Helmut Abels

arxiv:1512.08795 v2 · 2015-12-29 · math.FA · math.AP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MIT32RYLJWJFNZTFHZ4JCQ2F4R}

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	2026-05-18T01:23:22.376622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6227bd470b4d9256e6653e78914345e47ea84a7efc0717d4c4b748468ccdb23c

Aliases

arxiv: 1512.08795 · arxiv_version: 1512.08795v2 · doi: 10.48550/arxiv.1512.08795 · pith_short_12: MIT32RYLJWJF · pith_short_16: MIT32RYLJWJFNZTF · pith_short_8: MIT32RYL

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/MIT32RYLJWJFNZTFHZ4JCQ2F4R \
  | 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: 6227bd470b4d9256e6653e78914345e47ea84a7efc0717d4c4b748468ccdb23c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d86e6234f3d65e43111a8e8912c6a9817a1e9ad45a18f1121a347b3bbb7d15a",
    "cross_cats_sorted": [
      "math.AP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-12-29T21:11:50Z",
    "title_canon_sha256": "64f50bac4c449c48eeadcb7b76c017cf1dd0f69121b6533fd5fadb7b2b5ac8f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08795",
    "kind": "arxiv",
    "version": 2
  }
}