Pith Number

pith:YLLILDDC

pith:2026:YLLILDDCPJ64Y33II3SCUDC5EQ

not attested not anchored not stored refs pending

Stationary phase with Cauchy singularity. A critical point of signature $(+,-)$

Christian Klein, Johannes Sj\"ostrand, Maher Zerzeri

arxiv:2601.16542 v2 · 2026-01-23 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YLLILDDCPJ64Y33II3SCUDC5EQ}

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	2026-05-20T00:05:40.934007Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2d6858c627a7dcc6f6846e42a0c5d2409f032dd7475d0a07827d8120b284a90

Aliases

arxiv: 2601.16542 · arxiv_version: 2601.16542v2 · doi: 10.48550/arxiv.2601.16542 · pith_short_12: YLLILDDCPJ64 · pith_short_16: YLLILDDCPJ64Y33I · pith_short_8: YLLILDDC

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/YLLILDDCPJ64Y33II3SCUDC5EQ \
  | 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: c2d6858c627a7dcc6f6846e42a0c5d2409f032dd7475d0a07827d8120b284a90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc5887975fdefe26d0ed7e1aa9a68128cf4a46197d50947410e313a205df1460",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-01-23T08:22:00Z",
    "title_canon_sha256": "a8f3624f4ef822866e85457bf3ac44efa9cb1308cf4ddee0195ba0df1409c1f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.16542",
    "kind": "arxiv",
    "version": 2
  }
}