{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BBL4LET2FRTVEC27UICAUULCWC","short_pith_number":"pith:BBL4LET2","canonical_record":{"source":{"id":"1512.04514","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-14T20:52:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d04f6a64ee85dfe9f7d796f1f399e1e791fa5cd25c3d4c9c90a557806c91b50c","abstract_canon_sha256":"597350b01465292046d8851fd729530d3ddd056f9e8db7099d912ed6344edb21"},"schema_version":"1.0"},"canonical_sha256":"0857c5927a2c67520b5fa2040a5162b0b9e591c8dc08e813fa29eed987b1e779","source":{"kind":"arxiv","id":"1512.04514","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04514","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04514v2","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04514","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"pith_short_12","alias_value":"BBL4LET2FRTV","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BBL4LET2FRTVEC27","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BBL4LET2","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BBL4LET2FRTVEC27UICAUULCWC","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04514","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-14T20:52:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d04f6a64ee85dfe9f7d796f1f399e1e791fa5cd25c3d4c9c90a557806c91b50c","abstract_canon_sha256":"597350b01465292046d8851fd729530d3ddd056f9e8db7099d912ed6344edb21"},"schema_version":"1.0"},"canonical_sha256":"0857c5927a2c67520b5fa2040a5162b0b9e591c8dc08e813fa29eed987b1e779","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:31.053254Z","signature_b64":"8bdyBehToIzJ97avsxRKm9Yzfg2IfynIoOhGk7O12uJnkR1tlwKkIw6oJsbLQBKq5NW9uCU1upsr6w6rDDbJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0857c5927a2c67520b5fa2040a5162b0b9e591c8dc08e813fa29eed987b1e779","last_reissued_at":"2026-05-18T01:08:31.052712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:31.052712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04514","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":"2026-05-18T01:08:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"trnwiX/EruYZa/YkPJAHB5xh0QLjeoio5YwjeuIO9NJsRkYtGVSLqjLiGhpftP53hMi9x/e6ZVwvzeaYDm3HAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:30:42.842863Z"},"content_sha256":"fd6f438ac6d08b84ea75a5392ba24c329146a148b936b48afd22b3d34ca01258","schema_version":"1.0","event_id":"sha256:fd6f438ac6d08b84ea75a5392ba24c329146a148b936b48afd22b3d34ca01258"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BBL4LET2FRTVEC27UICAUULCWC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Information Structures for Feedback Capacity of Channels with Memory and Transmission Cost: Stochastic Optimal Control & Variational Equalities-Part I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Charalambos D. Charalambous, Christos K. Kourtellaris","submitted_at":"2015-12-14T20:52:04Z","abstract_excerpt":"The Finite Transmission Feedback Information (FTFI) capacity is characterized for any class of channel conditional distributions $\\big\\{{\\bf P}_{B_i|B^{i-1}, A_i} :i=0, 1, \\ldots, n\\big\\}$ and $\\big\\{ {\\bf P}_{B_i|B_{i-M}^{i-1}, A_i} :i=0, 1, \\ldots, n\\big\\}$, where $M$ is the memory of the channel, $B^n {\\stackrel{\\triangle}{=}} \\{B_j: j=\\ldots, 0,1, \\ldots, n\\}$ are the channel outputs and $A^n{\\stackrel{\\triangle}{=}} \\{A_j: j=\\ldots, 0,1, \\ldots, n\\}$ are the channel inputs. The characterizations of FTFI capacity, are obtained by first identifying the information structures of the optimal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04514","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":"2026-05-18T01:08:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+t2UEeZIBw/BUK6X+oMdhotCUwZdFbFFE9yhAfGQ3SiayBF0e8SxwZ8MtnXvYLmen6hIPcyPIkuN839BEi+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:30:42.843211Z"},"content_sha256":"ec350f46d9c3ccfa286da71ec6c1948a588f802a5e1982a81eeab2f0253cafff","schema_version":"1.0","event_id":"sha256:ec350f46d9c3ccfa286da71ec6c1948a588f802a5e1982a81eeab2f0253cafff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBL4LET2FRTVEC27UICAUULCWC/bundle.json","state_url":"https://pith.science/pith/BBL4LET2FRTVEC27UICAUULCWC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBL4LET2FRTVEC27UICAUULCWC/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":"2026-06-03T17:30:42Z","links":{"resolver":"https://pith.science/pith/BBL4LET2FRTVEC27UICAUULCWC","bundle":"https://pith.science/pith/BBL4LET2FRTVEC27UICAUULCWC/bundle.json","state":"https://pith.science/pith/BBL4LET2FRTVEC27UICAUULCWC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBL4LET2FRTVEC27UICAUULCWC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BBL4LET2FRTVEC27UICAUULCWC","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":"597350b01465292046d8851fd729530d3ddd056f9e8db7099d912ed6344edb21","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-14T20:52:04Z","title_canon_sha256":"d04f6a64ee85dfe9f7d796f1f399e1e791fa5cd25c3d4c9c90a557806c91b50c"},"schema_version":"1.0","source":{"id":"1512.04514","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04514","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04514v2","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04514","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"pith_short_12","alias_value":"BBL4LET2FRTV","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BBL4LET2FRTVEC27","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BBL4LET2","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:ec350f46d9c3ccfa286da71ec6c1948a588f802a5e1982a81eeab2f0253cafff","target":"graph","created_at":"2026-05-18T01:08:31Z","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":"The Finite Transmission Feedback Information (FTFI) capacity is characterized for any class of channel conditional distributions $\\big\\{{\\bf P}_{B_i|B^{i-1}, A_i} :i=0, 1, \\ldots, n\\big\\}$ and $\\big\\{ {\\bf P}_{B_i|B_{i-M}^{i-1}, A_i} :i=0, 1, \\ldots, n\\big\\}$, where $M$ is the memory of the channel, $B^n {\\stackrel{\\triangle}{=}} \\{B_j: j=\\ldots, 0,1, \\ldots, n\\}$ are the channel outputs and $A^n{\\stackrel{\\triangle}{=}} \\{A_j: j=\\ldots, 0,1, \\ldots, n\\}$ are the channel inputs. The characterizations of FTFI capacity, are obtained by first identifying the information structures of the optimal ","authors_text":"Charalambos D. Charalambous, Christos K. Kourtellaris","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-14T20:52:04Z","title":"Information Structures for Feedback Capacity of Channels with Memory and Transmission Cost: Stochastic Optimal Control & Variational Equalities-Part I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04514","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:fd6f438ac6d08b84ea75a5392ba24c329146a148b936b48afd22b3d34ca01258","target":"record","created_at":"2026-05-18T01:08:31Z","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":"597350b01465292046d8851fd729530d3ddd056f9e8db7099d912ed6344edb21","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-14T20:52:04Z","title_canon_sha256":"d04f6a64ee85dfe9f7d796f1f399e1e791fa5cd25c3d4c9c90a557806c91b50c"},"schema_version":"1.0","source":{"id":"1512.04514","kind":"arxiv","version":2}},"canonical_sha256":"0857c5927a2c67520b5fa2040a5162b0b9e591c8dc08e813fa29eed987b1e779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0857c5927a2c67520b5fa2040a5162b0b9e591c8dc08e813fa29eed987b1e779","first_computed_at":"2026-05-18T01:08:31.052712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:31.052712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8bdyBehToIzJ97avsxRKm9Yzfg2IfynIoOhGk7O12uJnkR1tlwKkIw6oJsbLQBKq5NW9uCU1upsr6w6rDDbJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:31.053254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04514","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd6f438ac6d08b84ea75a5392ba24c329146a148b936b48afd22b3d34ca01258","sha256:ec350f46d9c3ccfa286da71ec6c1948a588f802a5e1982a81eeab2f0253cafff"],"state_sha256":"9f694454592a685512d84ace9427d33a39228e9883d572e84b556a2034614f01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O+becQQpMRDOP3FwsELQQsbNaW/0sYyUMCCoB2fP9BUvM+1MUgNQtpOjSdyEVSnb98AB5cg+vNwBxqEFIKItAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:30:42.845133Z","bundle_sha256":"d1e853a3c9e49a914c89bd906a7e6a8fe63dbd3aa4566fcb52b4f94d397b25c0"}}