{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NWFKFJNYS26OYIH4JNMOAHGUBD","short_pith_number":"pith:NWFKFJNY","canonical_record":{"source":{"id":"1512.03779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-11T20:02:43Z","cross_cats_sorted":[],"title_canon_sha256":"1199fa5658e38560075c69c951923969d007d46b52877b28d93507d62ed13e5f","abstract_canon_sha256":"304551bc707c2d3fb1787647791334175e9ef65baeb7592ee859631d9dc893dc"},"schema_version":"1.0"},"canonical_sha256":"6d8aa2a5b896bcec20fc4b58e01cd408d449983ddb72f566e66b5137d689b8f8","source":{"kind":"arxiv","id":"1512.03779","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03779","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03779v1","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03779","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"NWFKFJNYS26O","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NWFKFJNYS26OYIH4","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NWFKFJNY","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NWFKFJNYS26OYIH4JNMOAHGUBD","target":"record","payload":{"canonical_record":{"source":{"id":"1512.03779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-11T20:02:43Z","cross_cats_sorted":[],"title_canon_sha256":"1199fa5658e38560075c69c951923969d007d46b52877b28d93507d62ed13e5f","abstract_canon_sha256":"304551bc707c2d3fb1787647791334175e9ef65baeb7592ee859631d9dc893dc"},"schema_version":"1.0"},"canonical_sha256":"6d8aa2a5b896bcec20fc4b58e01cd408d449983ddb72f566e66b5137d689b8f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:31.374711Z","signature_b64":"OPCAM2uFnzvAjLR5yedBg7L1MvW9Ya9u9oC7Q3VBAU8hzmf0NSfyAzee3eOILqVPBMNTsoezNa9IxGsrDce8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d8aa2a5b896bcec20fc4b58e01cd408d449983ddb72f566e66b5137d689b8f8","last_reissued_at":"2026-05-18T01:24:31.374013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:31.374013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.03779","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":"2026-05-18T01:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z/pZm0henvrHKYABpsoZENO7T/lUNfIQ68x54nxCsDimm7d24/TYBiYy3R9a/qiqTUCP6dlyBSlfryMf6ovsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:34:34.244812Z"},"content_sha256":"bea6e3992c40bc24ac81e68bf8d7c992ac6effc7501fd741a842b77b5e4377a9","schema_version":"1.0","event_id":"sha256:bea6e3992c40bc24ac81e68bf8d7c992ac6effc7501fd741a842b77b5e4377a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NWFKFJNYS26OYIH4JNMOAHGUBD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On monoids of injective partial cofinite selfmaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Du\\v{s}an Repov\\v{s}, Oleg Gutik","submitted_at":"2015-12-11T20:02:43Z","abstract_excerpt":"We study the semigroup $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ of injective partial cofinite selfmaps of an infinite cardinal $\\lambda$. We show that $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ is a bisimple inverse semigroup and each chain of idempotents in $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ is contained in a bicyclic subsemigroup of $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$, we describe the Green relations on $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ and we prove that every non-trivial congruence on $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ is a group congruence. Also, we describe the structure of the quotient semigroup"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03779","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":"2026-05-18T01:24:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3R0ZL9d25L8o8KxwcPSDnp2cveFWCqmhVXLgFRE56BMpOnPHXykHLgg645CyntMw3eP2///xTs7PbOvMXx+7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:34:34.245667Z"},"content_sha256":"f87b92b0cf12251dbb1af7192b72510e5acf3374173a96df55c74aab93ab79ad","schema_version":"1.0","event_id":"sha256:f87b92b0cf12251dbb1af7192b72510e5acf3374173a96df55c74aab93ab79ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWFKFJNYS26OYIH4JNMOAHGUBD/bundle.json","state_url":"https://pith.science/pith/NWFKFJNYS26OYIH4JNMOAHGUBD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWFKFJNYS26OYIH4JNMOAHGUBD/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":"2026-05-31T04:34:34Z","links":{"resolver":"https://pith.science/pith/NWFKFJNYS26OYIH4JNMOAHGUBD","bundle":"https://pith.science/pith/NWFKFJNYS26OYIH4JNMOAHGUBD/bundle.json","state":"https://pith.science/pith/NWFKFJNYS26OYIH4JNMOAHGUBD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWFKFJNYS26OYIH4JNMOAHGUBD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NWFKFJNYS26OYIH4JNMOAHGUBD","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":"304551bc707c2d3fb1787647791334175e9ef65baeb7592ee859631d9dc893dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-11T20:02:43Z","title_canon_sha256":"1199fa5658e38560075c69c951923969d007d46b52877b28d93507d62ed13e5f"},"schema_version":"1.0","source":{"id":"1512.03779","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03779","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03779v1","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03779","created_at":"2026-05-18T01:24:31Z"},{"alias_kind":"pith_short_12","alias_value":"NWFKFJNYS26O","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NWFKFJNYS26OYIH4","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NWFKFJNY","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:f87b92b0cf12251dbb1af7192b72510e5acf3374173a96df55c74aab93ab79ad","target":"graph","created_at":"2026-05-18T01:24:31Z","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 study the semigroup $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ of injective partial cofinite selfmaps of an infinite cardinal $\\lambda$. We show that $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ is a bisimple inverse semigroup and each chain of idempotents in $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ is contained in a bicyclic subsemigroup of $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$, we describe the Green relations on $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ and we prove that every non-trivial congruence on $\\mathscr{I}^{\\mathrm{cf}}_\\lambda$ is a group congruence. Also, we describe the structure of the quotient semigroup","authors_text":"Du\\v{s}an Repov\\v{s}, Oleg Gutik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-11T20:02:43Z","title":"On monoids of injective partial cofinite selfmaps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03779","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:bea6e3992c40bc24ac81e68bf8d7c992ac6effc7501fd741a842b77b5e4377a9","target":"record","created_at":"2026-05-18T01:24:31Z","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":"304551bc707c2d3fb1787647791334175e9ef65baeb7592ee859631d9dc893dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-11T20:02:43Z","title_canon_sha256":"1199fa5658e38560075c69c951923969d007d46b52877b28d93507d62ed13e5f"},"schema_version":"1.0","source":{"id":"1512.03779","kind":"arxiv","version":1}},"canonical_sha256":"6d8aa2a5b896bcec20fc4b58e01cd408d449983ddb72f566e66b5137d689b8f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d8aa2a5b896bcec20fc4b58e01cd408d449983ddb72f566e66b5137d689b8f8","first_computed_at":"2026-05-18T01:24:31.374013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:31.374013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OPCAM2uFnzvAjLR5yedBg7L1MvW9Ya9u9oC7Q3VBAU8hzmf0NSfyAzee3eOILqVPBMNTsoezNa9IxGsrDce8Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:31.374711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03779","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bea6e3992c40bc24ac81e68bf8d7c992ac6effc7501fd741a842b77b5e4377a9","sha256:f87b92b0cf12251dbb1af7192b72510e5acf3374173a96df55c74aab93ab79ad"],"state_sha256":"cd0ae389ea1df9991e7297a7696009d4ae9f7a250f3d4ab0df059ed99665e9c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sG3Avl3g+M+omxcELhLchZGMyB+vLMbgNBnXNcLqRXVn0kZNu5x0cmMA2WttZ6rg0ydSo075segm2N16ZR7KCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:34:34.250623Z","bundle_sha256":"6189a0287375693e08d70581271e08270a4d531f74140752951f12e73cc576f8"}}