Pith Number

pith:SM2PTG6Y

pith:2021:SM2PTG6Y2ODRXPKGYL6BWOW5HG

not attested not anchored not stored refs pending

Lecture notes for pseudodifferential operators and microlocal analysis

Shiqi Ma

arxiv:2107.12839 v1 · 2021-07-27 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SM2PTG6Y2ODRXPKGYL6BWOW5HG}

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.

Cited by

1 paper in Pith

Quantitative Direct Sampling for Initial Acoustic Sources

Receipt and verification

First computed	2026-07-05T03:01:01.254038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9334f99bd8d3871bbd46c2fc1b3add398362a166f76f24670e246479c4fd6f19

Aliases

arxiv: 2107.12839 · arxiv_version: 2107.12839v1 · doi: 10.48550/arxiv.2107.12839 · pith_short_12: SM2PTG6Y2ODR · pith_short_16: SM2PTG6Y2ODRXPKG · pith_short_8: SM2PTG6Y

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/SM2PTG6Y2ODRXPKGYL6BWOW5HG \
  | 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: 9334f99bd8d3871bbd46c2fc1b3add398362a166f76f24670e246479c4fd6f19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba29da229e072dc3fcbda060a55100b6dec614df806688fac2051bcc8c24bcc4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-07-27T14:17:00Z",
    "title_canon_sha256": "f795e8f8a6866ed1c398e34abb2ac5f096f68555505807668489258bfc351a4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.12839",
    "kind": "arxiv",
    "version": 1
  }
}