Pith Number

pith:WCO2QCNB

pith:2015:WCO2QCNBVJXIUAEDZ52W5XI7DV

not attested not anchored not stored refs pending

Multiplier ideal sheaves, complex singularity exponents, and restriction formula

Qi'an Guan

arxiv:1510.03586 v3 · 2015-10-13 · math.CV · 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{WCO2QCNBVJXIUAEDZ52W5XI7DV}

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	2026-05-18T01:29:20.365202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b09da809a1aa6e8a0083cf756edd1f1d76d63d810a427a69d62a6f7ddd33b988

Aliases

arxiv: 1510.03586 · arxiv_version: 1510.03586v3 · doi: 10.48550/arxiv.1510.03586 · pith_short_12: WCO2QCNBVJXI · pith_short_16: WCO2QCNBVJXIUAED · pith_short_8: WCO2QCNB

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/WCO2QCNBVJXIUAEDZ52W5XI7DV \
  | 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: b09da809a1aa6e8a0083cf756edd1f1d76d63d810a427a69d62a6f7ddd33b988

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad8ca7fc9344609f7235f43262fde1ba98aeeb8f1713cd71f677b423844a653e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2015-10-13T09:22:43Z",
    "title_canon_sha256": "b7c8ededf2dff31e3482ff35ca0b5fd62a5f71c4698bd04c90fb23a03467dd20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03586",
    "kind": "arxiv",
    "version": 3
  }
}