Pith Number

pith:OHUPUWCU

pith:2012:OHUPUWCUV27TTDULFWCWUCBH7E

not attested not anchored not stored refs pending

Bifurcation results for critical points of families of functionals

Alessandro Portaluri, Nils Waterstraat

arxiv:1210.0417 v1 · 2012-09-28 · math.DG · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OHUPUWCUV27TTDULFWCWUCBH7E}

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	2026-05-18T02:56:11.759873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71e8fa5854aebf398e8b2d856a0827f93ab22e8290715de51b578872d4a7dad4

Aliases

arxiv: 1210.0417 · arxiv_version: 1210.0417v1 · doi: 10.48550/arxiv.1210.0417 · pith_short_12: OHUPUWCUV27T · pith_short_16: OHUPUWCUV27TTDUL · pith_short_8: OHUPUWCU

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/OHUPUWCUV27TTDULFWCWUCBH7E \
  | 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: 71e8fa5854aebf398e8b2d856a0827f93ab22e8290715de51b578872d4a7dad4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d866d0ca8dcd19e0dd6d7e9a2ad99101829a0e92f62c70d51bc913641a1c922",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-09-28T12:29:12Z",
    "title_canon_sha256": "79ec1b9ae6e92d08c76c98660b7f6a2db992221d9831f79ed260f054bc13f57a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0417",
    "kind": "arxiv",
    "version": 1
  }
}