Pith Number

pith:FJF7SZWR

pith:2017:FJF7SZWRKWCEUTKVGQGMTXE4J5

not attested not anchored not stored refs pending

A note on the Morse index of 2k-ended phase transitions in R^2

Christos Mantoulidis

arxiv:1705.07580 v2 · 2017-05-22 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FJF7SZWRKWCEUTKVGQGMTXE4J5}

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	2026-05-18T00:37:47.333654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a4bf966d155844a4d55340cc9dc9c4f4a93d238d50bd06fa071ef97230e15d5

Aliases

arxiv: 1705.07580 · arxiv_version: 1705.07580v2 · doi: 10.48550/arxiv.1705.07580 · pith_short_12: FJF7SZWRKWCE · pith_short_16: FJF7SZWRKWCEUTKV · pith_short_8: FJF7SZWR

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/FJF7SZWRKWCEUTKVGQGMTXE4J5 \
  | 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: 2a4bf966d155844a4d55340cc9dc9c4f4a93d238d50bd06fa071ef97230e15d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95762f4a78bbd6f7bb9a2ac568049f333b2c34b26550bf5d326d8ca81d5132cf",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-05-22T06:59:41Z",
    "title_canon_sha256": "1b26e35465e26e757595aa64bd20dfaba7c2f08a905b66322cc2a6bcc420adc5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.07580",
    "kind": "arxiv",
    "version": 2
  }
}