Pith Number

pith:7YEGLUKX

pith:2012:7YEGLUKXUDTRUMOZYUDXLS6ANP

not attested not anchored not stored refs pending

Gradient trajectories for plane singular metrics I: oscillating trajectories

Vincent Grandjean

arxiv:1205.6749 v1 · 2012-05-30 · math.CA · math.AG · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7YEGLUKXUDTRUMOZYUDXLS6ANP}

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	2026-05-18T03:54:38.035833Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe0865d157a0e71a31d9c50775cbc06bf9bb24e22738995a0917165cd8780506

Aliases

arxiv: 1205.6749 · arxiv_version: 1205.6749v1 · doi: 10.48550/arxiv.1205.6749 · pith_short_12: 7YEGLUKXUDTR · pith_short_16: 7YEGLUKXUDTRUMOZ · pith_short_8: 7YEGLUKX

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/7YEGLUKXUDTRUMOZYUDXLS6ANP \
  | 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: fe0865d157a0e71a31d9c50775cbc06bf9bb24e22738995a0917165cd8780506

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55b0b93a5c0e38041eaf285f23624ffd7d73cfb0dfa0e5c83642ca0c61a08f73",
    "cross_cats_sorted": [
      "math.AG",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-05-30T16:38:21Z",
    "title_canon_sha256": "57019d6de39973417353f6a7235fa21680ebca8e72a4cc6fd77ee8fb8082c0f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.6749",
    "kind": "arxiv",
    "version": 1
  }
}