Pith Number

pith:Z7I7NT34

pith:2011:Z7I7NT34HWJ3YDBYKYUUGTM6M6

not attested not anchored not stored refs pending

Entire Parabolic Trajectories as Minimal Phase Transitions

Gianmaria Verzini, Susanna Terracini, Vivina Barutello

arxiv:1105.3358 v1 · 2011-05-17 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z7I7NT34HWJ3YDBYKYUUGTM6M6}

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	2026-05-18T02:21:59.782559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfd1f6cf7c3d93bc0c385629434d9e67b272af47055a5c23d996ca1e38a09d54

Aliases

arxiv: 1105.3358 · arxiv_version: 1105.3358v1 · doi: 10.48550/arxiv.1105.3358 · pith_short_12: Z7I7NT34HWJ3 · pith_short_16: Z7I7NT34HWJ3YDBY · pith_short_8: Z7I7NT34

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/Z7I7NT34HWJ3YDBYKYUUGTM6M6 \
  | 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: cfd1f6cf7c3d93bc0c385629434d9e67b272af47055a5c23d996ca1e38a09d54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e25e697cb8cb6b5150b9a85959e133634d7ec3db36050b4df01c57dc79d5bcf7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-05-17T12:56:08Z",
    "title_canon_sha256": "f8f229ff648f9966a5627e2f4535fd14e7069094b4668992284c2901b0f358cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.3358",
    "kind": "arxiv",
    "version": 1
  }
}