{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TNVCOSWHDD6OE3LIQRQU7ANB7W","short_pith_number":"pith:TNVCOSWH","canonical_record":{"source":{"id":"1503.03700","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-12T12:52:19Z","cross_cats_sorted":[],"title_canon_sha256":"540b073c854bdc8e942af5e5df95c31e86df0a424bbdf13030529ed8d7e032dd","abstract_canon_sha256":"2460ecc5b25e34e0b58de65ffdb456b95c6000f99dae7cf5b1d9066a67db4c6a"},"schema_version":"1.0"},"canonical_sha256":"9b6a274ac718fce26d6884614f81a1fd92fa114a7f37638f19eea131fefcab62","source":{"kind":"arxiv","id":"1503.03700","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03700","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03700v2","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03700","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"TNVCOSWHDD6O","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNVCOSWHDD6OE3LI","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNVCOSWH","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TNVCOSWHDD6OE3LIQRQU7ANB7W","target":"record","payload":{"canonical_record":{"source":{"id":"1503.03700","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-12T12:52:19Z","cross_cats_sorted":[],"title_canon_sha256":"540b073c854bdc8e942af5e5df95c31e86df0a424bbdf13030529ed8d7e032dd","abstract_canon_sha256":"2460ecc5b25e34e0b58de65ffdb456b95c6000f99dae7cf5b1d9066a67db4c6a"},"schema_version":"1.0"},"canonical_sha256":"9b6a274ac718fce26d6884614f81a1fd92fa114a7f37638f19eea131fefcab62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:27.835326Z","signature_b64":"k5QxlzhadtODJbeyNxTHwLUByQGRpPB1KJf5nJkRTzOZ4lCC5d2f1cCcVi+0fHv9kEB4ech/Q+jV0NouJ22oCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b6a274ac718fce26d6884614f81a1fd92fa114a7f37638f19eea131fefcab62","last_reissued_at":"2026-05-18T00:59:27.834766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:27.834766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.03700","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":"2026-05-18T00:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FwPTPKLoev8Gi68ptGEViN8LEtuibJZNLVkyGUDUG6i6XOCoSscoeDmp4FllJq7t5HPE7BjICpRivmN1HtZEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:55:14.302898Z"},"content_sha256":"172fb1ef0486c9b3ac6d3885f6c56bf03a06e7f3db091ff166477d2fd4bdf9f3","schema_version":"1.0","event_id":"sha256:172fb1ef0486c9b3ac6d3885f6c56bf03a06e7f3db091ff166477d2fd4bdf9f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TNVCOSWHDD6OE3LIQRQU7ANB7W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological equivalences for one-parameter bifurcations of maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Francisco Balibrea, Henrique M. Oliveira, Jose C. Valverde","submitted_at":"2015-03-12T12:52:19Z","abstract_excerpt":"Homeomorphisms allowing us to prove topological equivalences between one-parameter families of maps undergoing the same bifurcation are constructed in this paper. This provides a solution for a classical problem in bifurcation theory that was set out three decades ago and remained unexpectedly unpublished until now"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03700","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":"2026-05-18T00:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nzsBoHu321VBe3xh4c2GpPyA9njA/mmeSeI/ADrCco+4Fc4LU5Pa2WaoUxpv1zxg2wy35Ugwmcqt7PGGQlepAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:55:14.303231Z"},"content_sha256":"aa7f62450e52c6e3ed5f3324f8b99bc35ac9fb4735e77300e3fe96d69fc520e0","schema_version":"1.0","event_id":"sha256:aa7f62450e52c6e3ed5f3324f8b99bc35ac9fb4735e77300e3fe96d69fc520e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNVCOSWHDD6OE3LIQRQU7ANB7W/bundle.json","state_url":"https://pith.science/pith/TNVCOSWHDD6OE3LIQRQU7ANB7W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNVCOSWHDD6OE3LIQRQU7ANB7W/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":"2026-06-27T08:55:14Z","links":{"resolver":"https://pith.science/pith/TNVCOSWHDD6OE3LIQRQU7ANB7W","bundle":"https://pith.science/pith/TNVCOSWHDD6OE3LIQRQU7ANB7W/bundle.json","state":"https://pith.science/pith/TNVCOSWHDD6OE3LIQRQU7ANB7W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNVCOSWHDD6OE3LIQRQU7ANB7W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TNVCOSWHDD6OE3LIQRQU7ANB7W","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":"2460ecc5b25e34e0b58de65ffdb456b95c6000f99dae7cf5b1d9066a67db4c6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-12T12:52:19Z","title_canon_sha256":"540b073c854bdc8e942af5e5df95c31e86df0a424bbdf13030529ed8d7e032dd"},"schema_version":"1.0","source":{"id":"1503.03700","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03700","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03700v2","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03700","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"TNVCOSWHDD6O","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNVCOSWHDD6OE3LI","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNVCOSWH","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:aa7f62450e52c6e3ed5f3324f8b99bc35ac9fb4735e77300e3fe96d69fc520e0","target":"graph","created_at":"2026-05-18T00:59:27Z","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":"Homeomorphisms allowing us to prove topological equivalences between one-parameter families of maps undergoing the same bifurcation are constructed in this paper. This provides a solution for a classical problem in bifurcation theory that was set out three decades ago and remained unexpectedly unpublished until now","authors_text":"Francisco Balibrea, Henrique M. Oliveira, Jose C. Valverde","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-12T12:52:19Z","title":"Topological equivalences for one-parameter bifurcations of maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03700","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":"sha256:172fb1ef0486c9b3ac6d3885f6c56bf03a06e7f3db091ff166477d2fd4bdf9f3","target":"record","created_at":"2026-05-18T00:59:27Z","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":"2460ecc5b25e34e0b58de65ffdb456b95c6000f99dae7cf5b1d9066a67db4c6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-12T12:52:19Z","title_canon_sha256":"540b073c854bdc8e942af5e5df95c31e86df0a424bbdf13030529ed8d7e032dd"},"schema_version":"1.0","source":{"id":"1503.03700","kind":"arxiv","version":2}},"canonical_sha256":"9b6a274ac718fce26d6884614f81a1fd92fa114a7f37638f19eea131fefcab62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b6a274ac718fce26d6884614f81a1fd92fa114a7f37638f19eea131fefcab62","first_computed_at":"2026-05-18T00:59:27.834766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:27.834766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k5QxlzhadtODJbeyNxTHwLUByQGRpPB1KJf5nJkRTzOZ4lCC5d2f1cCcVi+0fHv9kEB4ech/Q+jV0NouJ22oCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:27.835326Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03700","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:172fb1ef0486c9b3ac6d3885f6c56bf03a06e7f3db091ff166477d2fd4bdf9f3","sha256:aa7f62450e52c6e3ed5f3324f8b99bc35ac9fb4735e77300e3fe96d69fc520e0"],"state_sha256":"657cb0c02f29c01b46e04a35fd3aac50adafbee847b606048ead864843752647"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qQ1msPnv3Tv/Wm4dVdLKGJEu4avZjVMVKtJQU5kl0e9GUhd9G8Jh9AN/fN2Pc7X+2Pmlwc5SgDPO92ggoXHWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T08:55:14.305363Z","bundle_sha256":"5c56bf732f26bd382aec023b905c6d2c4d62a91e67f34e6ba697acf2d4a34516"}}