{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MH7TCBCAG6Z7KGP6WUSTPSZ4H2","short_pith_number":"pith:MH7TCBCA","canonical_record":{"source":{"id":"1801.10007","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-30T14:28:32Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b66695bc63baeeb69c8a4a3b14360c0db42a40e9e7f81beca0c2e8ce943e8e0f","abstract_canon_sha256":"1c2da4103cbf00109e6687bb93f0af538a83b31d1c845e0025c85d4fd975283d"},"schema_version":"1.0"},"canonical_sha256":"61ff31044037b3f519feb52537cb3c3eb32bae20c546f7c05e39b48ba4821455","source":{"kind":"arxiv","id":"1801.10007","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10007","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10007v2","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10007","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"pith_short_12","alias_value":"MH7TCBCAG6Z7","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MH7TCBCAG6Z7KGP6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MH7TCBCA","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MH7TCBCAG6Z7KGP6WUSTPSZ4H2","target":"record","payload":{"canonical_record":{"source":{"id":"1801.10007","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-30T14:28:32Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b66695bc63baeeb69c8a4a3b14360c0db42a40e9e7f81beca0c2e8ce943e8e0f","abstract_canon_sha256":"1c2da4103cbf00109e6687bb93f0af538a83b31d1c845e0025c85d4fd975283d"},"schema_version":"1.0"},"canonical_sha256":"61ff31044037b3f519feb52537cb3c3eb32bae20c546f7c05e39b48ba4821455","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:58.170425Z","signature_b64":"T1MF0wO+6Pt7nB1gVjJKSmkNdxcZzf4sOiFGcG7WsSy6xd4xPtMbJpsMUyHRCIye+8jx3H0HtKO/o/BoJen2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61ff31044037b3f519feb52537cb3c3eb32bae20c546f7c05e39b48ba4821455","last_reissued_at":"2026-05-17T23:45:58.169889Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:58.169889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.10007","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":"2026-05-17T23:45:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8fGy+4bswFF6yku3NbgQwrVjxEWoff99kpUu1ivDtbUAEGylNdjVKIuS+XvVGbup7bA6KEKoEjGIWIqVInbSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T13:48:22.257285Z"},"content_sha256":"2cdfb41b53e506a0c8505ff153f4681854c3a64feab81ac8fa7c8879daffc6bf","schema_version":"1.0","event_id":"sha256:2cdfb41b53e506a0c8505ff153f4681854c3a64feab81ac8fa7c8879daffc6bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MH7TCBCAG6Z7KGP6WUSTPSZ4H2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pattern occurrences in random planar maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Benedikt Stufler, Michael Drmota","submitted_at":"2018-01-30T14:28:32Z","abstract_excerpt":"We consider planar maps adjusted with a (regular critical) Boltzmann distribution and show that the expected number of pattern occurrences of a given map is asymptotically linear when the number n of edges goes to infinity. The main ingredient for the proof is an extension of a formula by Liskovets (1999)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10007","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":"2026-05-17T23:45:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jp21LKvhHn0y2F3xQ4RMPwgwbFa9NpcZX4IlSKiBW9cm9tRprllavTzIiDmOQeCZ3O20Mj6h/rNE4AfhmwG+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T13:48:22.257649Z"},"content_sha256":"fa343b73cb21e657d553395c462e962df14efcb8f9e6c9df2288785781a45ba9","schema_version":"1.0","event_id":"sha256:fa343b73cb21e657d553395c462e962df14efcb8f9e6c9df2288785781a45ba9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MH7TCBCAG6Z7KGP6WUSTPSZ4H2/bundle.json","state_url":"https://pith.science/pith/MH7TCBCAG6Z7KGP6WUSTPSZ4H2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MH7TCBCAG6Z7KGP6WUSTPSZ4H2/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":"2026-07-01T13:48:22Z","links":{"resolver":"https://pith.science/pith/MH7TCBCAG6Z7KGP6WUSTPSZ4H2","bundle":"https://pith.science/pith/MH7TCBCAG6Z7KGP6WUSTPSZ4H2/bundle.json","state":"https://pith.science/pith/MH7TCBCAG6Z7KGP6WUSTPSZ4H2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MH7TCBCAG6Z7KGP6WUSTPSZ4H2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MH7TCBCAG6Z7KGP6WUSTPSZ4H2","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":"1c2da4103cbf00109e6687bb93f0af538a83b31d1c845e0025c85d4fd975283d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-30T14:28:32Z","title_canon_sha256":"b66695bc63baeeb69c8a4a3b14360c0db42a40e9e7f81beca0c2e8ce943e8e0f"},"schema_version":"1.0","source":{"id":"1801.10007","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10007","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10007v2","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10007","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"pith_short_12","alias_value":"MH7TCBCAG6Z7","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MH7TCBCAG6Z7KGP6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MH7TCBCA","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:fa343b73cb21e657d553395c462e962df14efcb8f9e6c9df2288785781a45ba9","target":"graph","created_at":"2026-05-17T23:45:58Z","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 consider planar maps adjusted with a (regular critical) Boltzmann distribution and show that the expected number of pattern occurrences of a given map is asymptotically linear when the number n of edges goes to infinity. The main ingredient for the proof is an extension of a formula by Liskovets (1999).","authors_text":"Benedikt Stufler, Michael Drmota","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-30T14:28:32Z","title":"Pattern occurrences in random planar maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10007","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":"sha256:2cdfb41b53e506a0c8505ff153f4681854c3a64feab81ac8fa7c8879daffc6bf","target":"record","created_at":"2026-05-17T23:45:58Z","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":"1c2da4103cbf00109e6687bb93f0af538a83b31d1c845e0025c85d4fd975283d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-30T14:28:32Z","title_canon_sha256":"b66695bc63baeeb69c8a4a3b14360c0db42a40e9e7f81beca0c2e8ce943e8e0f"},"schema_version":"1.0","source":{"id":"1801.10007","kind":"arxiv","version":2}},"canonical_sha256":"61ff31044037b3f519feb52537cb3c3eb32bae20c546f7c05e39b48ba4821455","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61ff31044037b3f519feb52537cb3c3eb32bae20c546f7c05e39b48ba4821455","first_computed_at":"2026-05-17T23:45:58.169889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:58.169889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T1MF0wO+6Pt7nB1gVjJKSmkNdxcZzf4sOiFGcG7WsSy6xd4xPtMbJpsMUyHRCIye+8jx3H0HtKO/o/BoJen2CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:58.170425Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.10007","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cdfb41b53e506a0c8505ff153f4681854c3a64feab81ac8fa7c8879daffc6bf","sha256:fa343b73cb21e657d553395c462e962df14efcb8f9e6c9df2288785781a45ba9"],"state_sha256":"4075283b5ffbc32c87e78bb0efbe0bae4f8857d0dea3b43bc9428e350b855894"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PBQh2HH5FOhJ2HyGWhSVBRnO4AfmXfVRA6Js+yY1HKC7eE7uTbsBqAMoKFGnAdkR7QyYbHuq9rtp9fhI3SpUBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T13:48:22.260460Z","bundle_sha256":"4fae9aa0382081d9ac5166230b0268ff01c28534ad4bf7ffdd16771108353a30"}}