{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XNLFXR75VNWQ2W5D2DU66MN3SQ","short_pith_number":"pith:XNLFXR75","canonical_record":{"source":{"id":"1708.07267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-24T03:28:36Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9cd607e544bbcf746df208b70af2059c081387dd1f0763c8bbf900b3a56de9ac","abstract_canon_sha256":"9912800bd1836aca97acc95e6c9cb492db8b3738b1f0b48a1bf9ed52545aa423"},"schema_version":"1.0"},"canonical_sha256":"bb565bc7fdab6d0d5ba3d0e9ef31bb9411ac52d670ccece7641916dfd595c029","source":{"kind":"arxiv","id":"1708.07267","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07267","created_at":"2026-05-18T00:36:46Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07267v1","created_at":"2026-05-18T00:36:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07267","created_at":"2026-05-18T00:36:46Z"},{"alias_kind":"pith_short_12","alias_value":"XNLFXR75VNWQ","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XNLFXR75VNWQ2W5D","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XNLFXR75","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XNLFXR75VNWQ2W5D2DU66MN3SQ","target":"record","payload":{"canonical_record":{"source":{"id":"1708.07267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-24T03:28:36Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9cd607e544bbcf746df208b70af2059c081387dd1f0763c8bbf900b3a56de9ac","abstract_canon_sha256":"9912800bd1836aca97acc95e6c9cb492db8b3738b1f0b48a1bf9ed52545aa423"},"schema_version":"1.0"},"canonical_sha256":"bb565bc7fdab6d0d5ba3d0e9ef31bb9411ac52d670ccece7641916dfd595c029","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:46.738551Z","signature_b64":"uo1u5rpnfyiP+PTgEKEPj4cgsobJYT4pMgiHEI/zGLQ1ti9wQO8BdV4xGAAMJcfmBrRAbq39or0LT2gpFLDEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb565bc7fdab6d0d5ba3d0e9ef31bb9411ac52d670ccece7641916dfd595c029","last_reissued_at":"2026-05-18T00:36:46.737975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:46.737975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.07267","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":"2026-05-18T00:36:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9mIugBAhyfTmfxx6uWgoa4oNsiAMZ+CJAkD2GgmuPYpBIcoNSPasSrqUmxIp4Ca4JrJxIjPEFWSTa/Ltt7OeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:27:46.342770Z"},"content_sha256":"c38b83941cac3c1b9fd07abdfbdce216b6c10e6495701fe6890989eb9691922b","schema_version":"1.0","event_id":"sha256:c38b83941cac3c1b9fd07abdfbdce216b6c10e6495701fe6890989eb9691922b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XNLFXR75VNWQ2W5D2DU66MN3SQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homology theory formulas for generalized Riemann-Hurwitz and generalized monoidal transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Alberto Verjovsky, James F. Glazebrook","submitted_at":"2017-08-24T03:28:36Z","abstract_excerpt":"In the context of orientable circuits and subcomplexes of these as representing certain singular spaces, we consider characteristic class formulas generalizing those classical results as seen for the Riemann-Hurwitz formula for regulating the topology of branched covering maps and that for monoidal transformations which include the standard blowing-up process. Here the results are presented as cap product pairings, which will be elements of a suitable homology theory, rather than characteristic numbers as would be the case when taking Kronecker products once Poincar\\'e duality is defined. We f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07267","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":"2026-05-18T00:36:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YFUKioE+nyvTgSI5RW/iVO43yPvVX3H/hkOxG5WsbzlJaNdHcXH7qlk3IJ+vZe5jHI9ZX/9wyCG8g0EYOCE2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:27:46.343106Z"},"content_sha256":"d57593b431ec1e48ad89ee569505fba730e4a11907014abc8dbbc60bafc6acb5","schema_version":"1.0","event_id":"sha256:d57593b431ec1e48ad89ee569505fba730e4a11907014abc8dbbc60bafc6acb5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNLFXR75VNWQ2W5D2DU66MN3SQ/bundle.json","state_url":"https://pith.science/pith/XNLFXR75VNWQ2W5D2DU66MN3SQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNLFXR75VNWQ2W5D2DU66MN3SQ/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":"2026-06-01T08:27:46Z","links":{"resolver":"https://pith.science/pith/XNLFXR75VNWQ2W5D2DU66MN3SQ","bundle":"https://pith.science/pith/XNLFXR75VNWQ2W5D2DU66MN3SQ/bundle.json","state":"https://pith.science/pith/XNLFXR75VNWQ2W5D2DU66MN3SQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNLFXR75VNWQ2W5D2DU66MN3SQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XNLFXR75VNWQ2W5D2DU66MN3SQ","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":"9912800bd1836aca97acc95e6c9cb492db8b3738b1f0b48a1bf9ed52545aa423","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-24T03:28:36Z","title_canon_sha256":"9cd607e544bbcf746df208b70af2059c081387dd1f0763c8bbf900b3a56de9ac"},"schema_version":"1.0","source":{"id":"1708.07267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07267","created_at":"2026-05-18T00:36:46Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07267v1","created_at":"2026-05-18T00:36:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07267","created_at":"2026-05-18T00:36:46Z"},{"alias_kind":"pith_short_12","alias_value":"XNLFXR75VNWQ","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XNLFXR75VNWQ2W5D","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XNLFXR75","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:d57593b431ec1e48ad89ee569505fba730e4a11907014abc8dbbc60bafc6acb5","target":"graph","created_at":"2026-05-18T00:36:46Z","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":"In the context of orientable circuits and subcomplexes of these as representing certain singular spaces, we consider characteristic class formulas generalizing those classical results as seen for the Riemann-Hurwitz formula for regulating the topology of branched covering maps and that for monoidal transformations which include the standard blowing-up process. Here the results are presented as cap product pairings, which will be elements of a suitable homology theory, rather than characteristic numbers as would be the case when taking Kronecker products once Poincar\\'e duality is defined. We f","authors_text":"Alberto Verjovsky, James F. Glazebrook","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-24T03:28:36Z","title":"Homology theory formulas for generalized Riemann-Hurwitz and generalized monoidal transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07267","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:c38b83941cac3c1b9fd07abdfbdce216b6c10e6495701fe6890989eb9691922b","target":"record","created_at":"2026-05-18T00:36:46Z","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":"9912800bd1836aca97acc95e6c9cb492db8b3738b1f0b48a1bf9ed52545aa423","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-24T03:28:36Z","title_canon_sha256":"9cd607e544bbcf746df208b70af2059c081387dd1f0763c8bbf900b3a56de9ac"},"schema_version":"1.0","source":{"id":"1708.07267","kind":"arxiv","version":1}},"canonical_sha256":"bb565bc7fdab6d0d5ba3d0e9ef31bb9411ac52d670ccece7641916dfd595c029","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb565bc7fdab6d0d5ba3d0e9ef31bb9411ac52d670ccece7641916dfd595c029","first_computed_at":"2026-05-18T00:36:46.737975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:46.737975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uo1u5rpnfyiP+PTgEKEPj4cgsobJYT4pMgiHEI/zGLQ1ti9wQO8BdV4xGAAMJcfmBrRAbq39or0LT2gpFLDEAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:46.738551Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c38b83941cac3c1b9fd07abdfbdce216b6c10e6495701fe6890989eb9691922b","sha256:d57593b431ec1e48ad89ee569505fba730e4a11907014abc8dbbc60bafc6acb5"],"state_sha256":"e39933e7d6954dadbc157a832e5b711fa66fa8dd5c881a75707141004013bddf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1vBUTq6E1xh+NHdUPJsGdY8Kh1lfW3pkyafOigaxsqwqzABxzTt8KOYItmE/GvjeCJt4SUWQuyvNiDedYBbCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:27:46.345136Z","bundle_sha256":"da1e248e89d2fc84b31a674c29e3a1a40aced62739fe693ac9ce602f39a96eea"}}