Pith Number

pith:VVRLLX5B

pith:2012:VVRLLX5BXXBEX5V7WQDOIWUX7C

not attested not anchored not stored refs pending

Three lectures on Algebraic Microlocal Analysis

Pierre Schapira

arxiv:1206.1435 v3 · 2012-06-07 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VVRLLX5BXXBEX5V7WQDOIWUX7C}

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	2026-05-18T03:04:24.342330Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad62b5dfa1bdc24bf6bfb406e45a97f880efe206774371ede27eafc67c0a5c50

Aliases

arxiv: 1206.1435 · arxiv_version: 1206.1435v3 · doi: 10.48550/arxiv.1206.1435 · pith_short_12: VVRLLX5BXXBE · pith_short_16: VVRLLX5BXXBEX5V7 · pith_short_8: VVRLLX5B

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/VVRLLX5BXXBEX5V7WQDOIWUX7C \
  | 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: ad62b5dfa1bdc24bf6bfb406e45a97f880efe206774371ede27eafc67c0a5c50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9799f3c13ec81edfa11b8c6deb38166fb56949ca4a5a2261ff807a861e89809e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-06-07T10:04:35Z",
    "title_canon_sha256": "92a5042240a373bfcb8644c0ccfee9b809d75d121eceb56b76f4b3735281b97c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1435",
    "kind": "arxiv",
    "version": 3
  }
}