Pith Number

pith:IXJILCUE

pith:2011:IXJILCUEUSOXWMNGYX5FGDTZG6

not attested not anchored not stored refs pending

Finding saddle points of mountain pass type with quadratic models on affine spaces

C.H. Jeffrey Pang

arxiv:1107.4287 v2 · 2011-07-21 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IXJILCUEUSOXWMNGYX5FGDTZG6}

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	2026-05-18T03:40:36.781174Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45d2858a84a49d7b31a6c5fa530e79379788e9ee86a0c7e9117e5996452576ff

Aliases

arxiv: 1107.4287 · arxiv_version: 1107.4287v2 · doi: 10.48550/arxiv.1107.4287 · pith_short_12: IXJILCUEUSOX · pith_short_16: IXJILCUEUSOXWMNG · pith_short_8: IXJILCUE

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/IXJILCUEUSOXWMNGYX5FGDTZG6 \
  | 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: 45d2858a84a49d7b31a6c5fa530e79379788e9ee86a0c7e9117e5996452576ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "604e15ef8cac007406217d58f82e8005149145d82e41f631777841ebed6fb512",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2011-07-21T14:41:01Z",
    "title_canon_sha256": "67ce544c85a619c246cc2f8fc9b4a149b4e08a621cd7683c951c39437769c944"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4287",
    "kind": "arxiv",
    "version": 2
  }
}