{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:APGQZ7CMYRPYE5VVYXL7AZWZVL","short_pith_number":"pith:APGQZ7CM","canonical_record":{"source":{"id":"1503.08322","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.NE","submitted_at":"2015-03-28T16:33:20Z","cross_cats_sorted":[],"title_canon_sha256":"df73f9659bde3d4474565f187854c0b46267a707f9fc32beed8b7e7d3df523b7","abstract_canon_sha256":"287b152973046ac12b5f0079fa4cfd4fc7cc10c82e17bd783f2b0e0d67e3250d"},"schema_version":"1.0"},"canonical_sha256":"03cd0cfc4cc45f8276b5c5d7f066d9aac0d61229095b632d9739e0969985c993","source":{"kind":"arxiv","id":"1503.08322","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08322","created_at":"2026-05-18T01:24:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08322v1","created_at":"2026-05-18T01:24:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08322","created_at":"2026-05-18T01:24:25Z"},{"alias_kind":"pith_short_12","alias_value":"APGQZ7CMYRPY","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"APGQZ7CMYRPYE5VV","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"APGQZ7CM","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:APGQZ7CMYRPYE5VVYXL7AZWZVL","target":"record","payload":{"canonical_record":{"source":{"id":"1503.08322","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.NE","submitted_at":"2015-03-28T16:33:20Z","cross_cats_sorted":[],"title_canon_sha256":"df73f9659bde3d4474565f187854c0b46267a707f9fc32beed8b7e7d3df523b7","abstract_canon_sha256":"287b152973046ac12b5f0079fa4cfd4fc7cc10c82e17bd783f2b0e0d67e3250d"},"schema_version":"1.0"},"canonical_sha256":"03cd0cfc4cc45f8276b5c5d7f066d9aac0d61229095b632d9739e0969985c993","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:25.033859Z","signature_b64":"3VMpi3CoFGAXM5ApGMpmewvQH6/CCy1QYj29pPpfEEfEqMWOaSQZCc9iBzGf0lOjN7Uz0W+B7FswoB7tMk+fCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03cd0cfc4cc45f8276b5c5d7f066d9aac0d61229095b632d9739e0969985c993","last_reissued_at":"2026-05-18T01:24:25.033188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:25.033188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.08322","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"614W7129KqGqXwsb3BD0E3DrWLtv5uY5QV/AGHLlg4ecr6iZLvfHHYieWIxOFesyQKCmmkMo+HVpGqBq+9rsDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:52:09.967508Z"},"content_sha256":"1be12e55aaaeb3dba47791fa8010550e803ee11640eb6cc81bc781551706f8ce","schema_version":"1.0","event_id":"sha256:1be12e55aaaeb3dba47791fa8010550e803ee11640eb6cc81bc781551706f8ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:APGQZ7CMYRPYE5VVYXL7AZWZVL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Further Evidence about Magnification and Shape in Neural Gas","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.NE","authors_text":"Andrea Pedrini, Giacomo Parigi, Marco Piastra","submitted_at":"2015-03-28T16:33:20Z","abstract_excerpt":"Neural gas (NG) is a robust vector quantization algorithm with a well-known mathematical model. According to this, the neural gas samples the underlying data distribution following a power law with a magnification exponent that depends on data dimensionality only. The effects of shape in the input data distribution, however, are not entirely covered by the NG model above, due to the technical difficulties involved. The experimental work described here shows that shape is indeed relevant in determining the overall NG behavior; in particular, some experiments reveal richer and complex behaviors "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08322","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U7xxL49TXDdrIWZOM7rAaRi+mWJxXvMVFKJAt+pC2RcCyIejG+v/VzrPl7TKUDHGfxxgLDoPJGZwDYzqPfCTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:52:09.967899Z"},"content_sha256":"7509eb8402995061c0bfd65f2f1f7f73d26139283471f37c298ccdb65f292372","schema_version":"1.0","event_id":"sha256:7509eb8402995061c0bfd65f2f1f7f73d26139283471f37c298ccdb65f292372"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/APGQZ7CMYRPYE5VVYXL7AZWZVL/bundle.json","state_url":"https://pith.science/pith/APGQZ7CMYRPYE5VVYXL7AZWZVL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/APGQZ7CMYRPYE5VVYXL7AZWZVL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T21:52:09Z","links":{"resolver":"https://pith.science/pith/APGQZ7CMYRPYE5VVYXL7AZWZVL","bundle":"https://pith.science/pith/APGQZ7CMYRPYE5VVYXL7AZWZVL/bundle.json","state":"https://pith.science/pith/APGQZ7CMYRPYE5VVYXL7AZWZVL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/APGQZ7CMYRPYE5VVYXL7AZWZVL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:APGQZ7CMYRPYE5VVYXL7AZWZVL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"287b152973046ac12b5f0079fa4cfd4fc7cc10c82e17bd783f2b0e0d67e3250d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.NE","submitted_at":"2015-03-28T16:33:20Z","title_canon_sha256":"df73f9659bde3d4474565f187854c0b46267a707f9fc32beed8b7e7d3df523b7"},"schema_version":"1.0","source":{"id":"1503.08322","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08322","created_at":"2026-05-18T01:24:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08322v1","created_at":"2026-05-18T01:24:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08322","created_at":"2026-05-18T01:24:25Z"},{"alias_kind":"pith_short_12","alias_value":"APGQZ7CMYRPY","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"APGQZ7CMYRPYE5VV","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"APGQZ7CM","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:7509eb8402995061c0bfd65f2f1f7f73d26139283471f37c298ccdb65f292372","target":"graph","created_at":"2026-05-18T01:24:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Neural gas (NG) is a robust vector quantization algorithm with a well-known mathematical model. According to this, the neural gas samples the underlying data distribution following a power law with a magnification exponent that depends on data dimensionality only. The effects of shape in the input data distribution, however, are not entirely covered by the NG model above, due to the technical difficulties involved. The experimental work described here shows that shape is indeed relevant in determining the overall NG behavior; in particular, some experiments reveal richer and complex behaviors ","authors_text":"Andrea Pedrini, Giacomo Parigi, Marco Piastra","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.NE","submitted_at":"2015-03-28T16:33:20Z","title":"Some Further Evidence about Magnification and Shape in Neural Gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08322","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1be12e55aaaeb3dba47791fa8010550e803ee11640eb6cc81bc781551706f8ce","target":"record","created_at":"2026-05-18T01:24:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"287b152973046ac12b5f0079fa4cfd4fc7cc10c82e17bd783f2b0e0d67e3250d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.NE","submitted_at":"2015-03-28T16:33:20Z","title_canon_sha256":"df73f9659bde3d4474565f187854c0b46267a707f9fc32beed8b7e7d3df523b7"},"schema_version":"1.0","source":{"id":"1503.08322","kind":"arxiv","version":1}},"canonical_sha256":"03cd0cfc4cc45f8276b5c5d7f066d9aac0d61229095b632d9739e0969985c993","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03cd0cfc4cc45f8276b5c5d7f066d9aac0d61229095b632d9739e0969985c993","first_computed_at":"2026-05-18T01:24:25.033188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:25.033188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3VMpi3CoFGAXM5ApGMpmewvQH6/CCy1QYj29pPpfEEfEqMWOaSQZCc9iBzGf0lOjN7Uz0W+B7FswoB7tMk+fCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:25.033859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08322","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1be12e55aaaeb3dba47791fa8010550e803ee11640eb6cc81bc781551706f8ce","sha256:7509eb8402995061c0bfd65f2f1f7f73d26139283471f37c298ccdb65f292372"],"state_sha256":"917dc366420299736e83108f51eb0bcfa9f1147dcff42c577f9a689277fbeb43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DlqryVdtZbu//c90tZb8reOCW9VXZa1UMAcdD27ikL2eyRY8kz14If/qHMPla8P2cFIbmpM0+U4ZJqdA+4WcBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:52:09.969955Z","bundle_sha256":"d1c58ae2a98d697df6967b2a65da43e8f6e29e2abc3d1eeb238b31069cbacf0b"}}