Pith Number

pith:KGTM7MMC

pith:2013:KGTM7MMCYNGW2RHRIL6IXBBFQ6

not attested not anchored not stored refs pending

Ambrosetti-Rabinowitz theorems revisited

Abdellaziz Harrabi

arxiv:1310.7743 v1 · 2013-10-29 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KGTM7MMCYNGW2RHRIL6IXBBFQ6}

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	2026-05-18T03:08:35.386699Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51a6cfb182c34d6d44f142fc8b842587b8883e9b8b274ffad64bc11d410939a3

Aliases

arxiv: 1310.7743 · arxiv_version: 1310.7743v1 · doi: 10.48550/arxiv.1310.7743 · pith_short_12: KGTM7MMCYNGW · pith_short_16: KGTM7MMCYNGW2RHR · pith_short_8: KGTM7MMC

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/KGTM7MMCYNGW2RHRIL6IXBBFQ6 \
  | 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: 51a6cfb182c34d6d44f142fc8b842587b8883e9b8b274ffad64bc11d410939a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d62352c5998d85c3ef673c6c5af977a187f2f577d65304dd26b095dba23b5252",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-10-29T10:28:05Z",
    "title_canon_sha256": "fdf96c9572a3e89e5d3d563abbbbbbbd0bec1cedf30a21c2f35952e115347342"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.7743",
    "kind": "arxiv",
    "version": 1
  }
}