Pith Number

pith:TPCSWCYQ

pith:2019:TPCSWCYQCH4JNA53BHHATEUV7H

not attested not anchored not stored refs pending

A monotonicity result under symmetry and Morse index constraints in the plane

Francesca Gladiali

arxiv:1904.03905 v1 · 2019-04-08 · 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{TPCSWCYQCH4JNA53BHHATEUV7H}

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	2026-05-17T23:49:07.743836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bc52b0b1011f89683bb09ce099295f9c4c289452644c4e66c30b43b129ced1b

Aliases

arxiv: 1904.03905 · arxiv_version: 1904.03905v1 · doi: 10.48550/arxiv.1904.03905 · pith_short_12: TPCSWCYQCH4J · pith_short_16: TPCSWCYQCH4JNA53 · pith_short_8: TPCSWCYQ

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/TPCSWCYQCH4JNA53BHHATEUV7H \
  | 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: 9bc52b0b1011f89683bb09ce099295f9c4c289452644c4e66c30b43b129ced1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbb9b4d17023babf4d92273639c4be16795ac01fd777bfd5a354e8c6265a9223",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-04-08T09:30:43Z",
    "title_canon_sha256": "7f5e9c13061ebfe2dec3febf861596378ba47ff25d3c1d89d4b7c5a49fd219eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.03905",
    "kind": "arxiv",
    "version": 1
  }
}