{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4KA4LRJA7OXESGN77WWVRSVLKN","short_pith_number":"pith:4KA4LRJA","canonical_record":{"source":{"id":"1703.09489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-28T10:06:45Z","cross_cats_sorted":[],"title_canon_sha256":"2939aedd41a4ec01613a7aedccdee217a68e1ed5430edb01c6751894a3346249","abstract_canon_sha256":"6e0d0213297e54b461211bd04f5ebc57c466033a9304db269fc3cd520acdda17"},"schema_version":"1.0"},"canonical_sha256":"e281c5c520fbae4919bffdad58caab5370dd70fb67f10479ef777c63be2ccd4d","source":{"kind":"arxiv","id":"1703.09489","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09489","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09489v2","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09489","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"pith_short_12","alias_value":"4KA4LRJA7OXE","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4KA4LRJA7OXESGN7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4KA4LRJA","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4KA4LRJA7OXESGN77WWVRSVLKN","target":"record","payload":{"canonical_record":{"source":{"id":"1703.09489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-28T10:06:45Z","cross_cats_sorted":[],"title_canon_sha256":"2939aedd41a4ec01613a7aedccdee217a68e1ed5430edb01c6751894a3346249","abstract_canon_sha256":"6e0d0213297e54b461211bd04f5ebc57c466033a9304db269fc3cd520acdda17"},"schema_version":"1.0"},"canonical_sha256":"e281c5c520fbae4919bffdad58caab5370dd70fb67f10479ef777c63be2ccd4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:01.264692Z","signature_b64":"VsDgYUyDZ26u85NQpkw4yQvbXWGhXzQ5/eetNyr0xiURO/sjnl/t6Wo18xho6RU+Xz0bjhmCBuucOEmX2Wh/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e281c5c520fbae4919bffdad58caab5370dd70fb67f10479ef777c63be2ccd4d","last_reissued_at":"2026-05-17T23:55:01.264309Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:01.264309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.09489","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wIx4Tsysh9j0/xpJxn+Y/2Os7zwcBbsedNt0pjnvbTXsC2ZBJWBEDSkxw4YQ8xYwX6K47hTtPjRMRc5npgMqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:04:31.970828Z"},"content_sha256":"51ffcd5dc60ad552e219c8150a30499511c84045d4be06c7b0d31feb62dc9429","schema_version":"1.0","event_id":"sha256:51ffcd5dc60ad552e219c8150a30499511c84045d4be06c7b0d31feb62dc9429"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4KA4LRJA7OXESGN77WWVRSVLKN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized connected sum formula for the Arnold invariants of generic plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Keiichi Sakai, Ryutaro Sugiyama","submitted_at":"2017-03-28T10:06:45Z","abstract_excerpt":"We define the generalized connected sum for generic closed plane curves, generalizing the strange sum defined by Arnold, and completely describe how the Arnold invariants $J^{\\pm}$ and $\\mathit{St}$ behave under the generalized connected sums."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09489","kind":"arxiv","version":2},"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":"2026-05-17T23:55:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OxPYx3ONaqgKnbGCbgh7Mpy8bpCzMJcGDLKF9ZjYhJehGNlCnEpGsHdQJS12dZlYgBbpxqsd8rZIigGGveceBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:04:31.971157Z"},"content_sha256":"0d608af561bce5b642134d404aada4b7767c72a83aec1658d05d196c4aba497f","schema_version":"1.0","event_id":"sha256:0d608af561bce5b642134d404aada4b7767c72a83aec1658d05d196c4aba497f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KA4LRJA7OXESGN77WWVRSVLKN/bundle.json","state_url":"https://pith.science/pith/4KA4LRJA7OXESGN77WWVRSVLKN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KA4LRJA7OXESGN77WWVRSVLKN/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":"2026-06-23T00:04:31Z","links":{"resolver":"https://pith.science/pith/4KA4LRJA7OXESGN77WWVRSVLKN","bundle":"https://pith.science/pith/4KA4LRJA7OXESGN77WWVRSVLKN/bundle.json","state":"https://pith.science/pith/4KA4LRJA7OXESGN77WWVRSVLKN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KA4LRJA7OXESGN77WWVRSVLKN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4KA4LRJA7OXESGN77WWVRSVLKN","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":"6e0d0213297e54b461211bd04f5ebc57c466033a9304db269fc3cd520acdda17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-28T10:06:45Z","title_canon_sha256":"2939aedd41a4ec01613a7aedccdee217a68e1ed5430edb01c6751894a3346249"},"schema_version":"1.0","source":{"id":"1703.09489","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09489","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09489v2","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09489","created_at":"2026-05-17T23:55:01Z"},{"alias_kind":"pith_short_12","alias_value":"4KA4LRJA7OXE","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4KA4LRJA7OXESGN7","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4KA4LRJA","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:0d608af561bce5b642134d404aada4b7767c72a83aec1658d05d196c4aba497f","target":"graph","created_at":"2026-05-17T23:55:01Z","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":"We define the generalized connected sum for generic closed plane curves, generalizing the strange sum defined by Arnold, and completely describe how the Arnold invariants $J^{\\pm}$ and $\\mathit{St}$ behave under the generalized connected sums.","authors_text":"Keiichi Sakai, Ryutaro Sugiyama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-28T10:06:45Z","title":"Generalized connected sum formula for the Arnold invariants of generic plane curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09489","kind":"arxiv","version":2},"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":"sha256:51ffcd5dc60ad552e219c8150a30499511c84045d4be06c7b0d31feb62dc9429","target":"record","created_at":"2026-05-17T23:55:01Z","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":"6e0d0213297e54b461211bd04f5ebc57c466033a9304db269fc3cd520acdda17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-03-28T10:06:45Z","title_canon_sha256":"2939aedd41a4ec01613a7aedccdee217a68e1ed5430edb01c6751894a3346249"},"schema_version":"1.0","source":{"id":"1703.09489","kind":"arxiv","version":2}},"canonical_sha256":"e281c5c520fbae4919bffdad58caab5370dd70fb67f10479ef777c63be2ccd4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e281c5c520fbae4919bffdad58caab5370dd70fb67f10479ef777c63be2ccd4d","first_computed_at":"2026-05-17T23:55:01.264309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:01.264309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VsDgYUyDZ26u85NQpkw4yQvbXWGhXzQ5/eetNyr0xiURO/sjnl/t6Wo18xho6RU+Xz0bjhmCBuucOEmX2Wh/Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:01.264692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.09489","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51ffcd5dc60ad552e219c8150a30499511c84045d4be06c7b0d31feb62dc9429","sha256:0d608af561bce5b642134d404aada4b7767c72a83aec1658d05d196c4aba497f"],"state_sha256":"56a5f6f58bd8b55d7097f26ae020c5cd1437d574506eb581623e80258aacdf65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RRbHI+DrRhTeVV4xIWfLXw4YZEdOpClV+36MBd5LYmv9dStWaqvtIOLCYwFUbyKMExvBbChAd1yh+fM9/mZ+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:04:31.973007Z","bundle_sha256":"de65f2c03870ddb2e408230363982b22527c7ec82980132c4ba945b89cb561f1"}}