Pith Number

pith:BWAYRAW5

pith:2017:BWAYRAW5R3MM5XII54BCE6AIR2

not attested not anchored not stored refs pending

Milnor and Tjurina numbers for a hypersurface germ with isolated singularity

Yongqiang Liu

arxiv:1708.09716 v2 · 2017-08-31 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BWAYRAW5R3MM5XII54BCE6AIR2}

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	2026-05-18T00:11:50.626365Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d818882dd8ed8cedd08ef022278088e87b68d7f2ddb0df65f3c62496a59d9c7

Aliases

arxiv: 1708.09716 · arxiv_version: 1708.09716v2 · doi: 10.48550/arxiv.1708.09716 · pith_short_12: BWAYRAW5R3MM · pith_short_16: BWAYRAW5R3MM5XII · pith_short_8: BWAYRAW5

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/BWAYRAW5R3MM5XII54BCE6AIR2 \
  | 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: 0d818882dd8ed8cedd08ef022278088e87b68d7f2ddb0df65f3c62496a59d9c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3461704fb8f0e07ab5998549c6d1f06122e7a4c7f61fde975eccc2e341426e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2017-08-31T14:01:36Z",
    "title_canon_sha256": "51fe6566d701bad5d735eab83972b8852184f2e91615214f8586906d64113021"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.09716",
    "kind": "arxiv",
    "version": 2
  }
}