{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:657P2WPD2RIOQHJMAWV4SXPMQN","short_pith_number":"pith:657P2WPD","canonical_record":{"source":{"id":"1405.2449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-10T16:34:34Z","cross_cats_sorted":[],"title_canon_sha256":"0ea97a872f005bb1b05d1005340925a080c4b77b142b90a7d7cfe0c32a1ed31c","abstract_canon_sha256":"4d6a0d5b8fd7786df62f3d4d3b82f6e951e78d53a8be3d3204b7f0edd27e56d7"},"schema_version":"1.0"},"canonical_sha256":"f77efd59e3d450e81d2c05abc95dec837b9a88c0d5603d5b0e2030a39f87c26a","source":{"kind":"arxiv","id":"1405.2449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2449","created_at":"2026-05-18T01:09:42Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2449v1","created_at":"2026-05-18T01:09:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2449","created_at":"2026-05-18T01:09:42Z"},{"alias_kind":"pith_short_12","alias_value":"657P2WPD2RIO","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"657P2WPD2RIOQHJM","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"657P2WPD","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:657P2WPD2RIOQHJMAWV4SXPMQN","target":"record","payload":{"canonical_record":{"source":{"id":"1405.2449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-10T16:34:34Z","cross_cats_sorted":[],"title_canon_sha256":"0ea97a872f005bb1b05d1005340925a080c4b77b142b90a7d7cfe0c32a1ed31c","abstract_canon_sha256":"4d6a0d5b8fd7786df62f3d4d3b82f6e951e78d53a8be3d3204b7f0edd27e56d7"},"schema_version":"1.0"},"canonical_sha256":"f77efd59e3d450e81d2c05abc95dec837b9a88c0d5603d5b0e2030a39f87c26a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:42.378710Z","signature_b64":"3UdSCAcNgyXUMtq91dz+OW5wYjRje4BNz1dK2FoBxBLAVYSCYKGUB/sVIg3eaYDwWOU8UeEOjxCYoOr8J2phCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f77efd59e3d450e81d2c05abc95dec837b9a88c0d5603d5b0e2030a39f87c26a","last_reissued_at":"2026-05-18T01:09:42.378243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:42.378243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.2449","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":"2026-05-18T01:09:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q44KooOYzf+AeyM/G7raSBAipyb4g7KDqdyZ0Lc14QGf7Y5JWHaZQaSQeCfzbxKz5W95DEVRN2qGznWO3xy/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:26:06.441737Z"},"content_sha256":"a2c473385290e1bcd65452ef5c5bf2d280a2d2e2fe4637ceeba27589fad2d87b","schema_version":"1.0","event_id":"sha256:a2c473385290e1bcd65452ef5c5bf2d280a2d2e2fe4637ceeba27589fad2d87b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:657P2WPD2RIOQHJMAWV4SXPMQN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strongly polynomial sequences as interpretations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Goodall, Jaroslav Nesetril, Patrice Ossona de Mendez","submitted_at":"2014-05-10T16:34:34Z","abstract_excerpt":"A strongly polynomial sequence of graphs $(G_n)$ is a sequence $(G_n)_{n\\in\\mathbb{N}}$ of finite graphs such that, for every graph $F$, the number of homomorphisms from $F$ to $G_n$ is a fixed polynomial function of $n$ (depending on $F$). For example, $(K_n)$ is strongly polynomial since the number of homomorphisms from $F$ to $K_n$ is the chromatic polynomial of $F$ evaluated at $n$. In earlier work of de la Harpe and Jaeger, and more recently of Averbouch, Garijo, Godlin, Goodall, Makowsky, Ne\\v{s}et\\v{r}il, Tittmann, Zilber and others, various examples of strongly polynomial sequences and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2449","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":"2026-05-18T01:09:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TakM9ge7M42GIQkrK08NBanII/fOvAAz/bitRgpFNZeuMMkb7hq+of8cl4wl9SILF1IBli+n/hsT3Hb6aGQFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:26:06.442107Z"},"content_sha256":"387738863722b9b87b5e1c8d34e8fa2b1ede08f228602f7e9d84eb649c924ab8","schema_version":"1.0","event_id":"sha256:387738863722b9b87b5e1c8d34e8fa2b1ede08f228602f7e9d84eb649c924ab8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/657P2WPD2RIOQHJMAWV4SXPMQN/bundle.json","state_url":"https://pith.science/pith/657P2WPD2RIOQHJMAWV4SXPMQN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/657P2WPD2RIOQHJMAWV4SXPMQN/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":"2026-06-02T08:26:06Z","links":{"resolver":"https://pith.science/pith/657P2WPD2RIOQHJMAWV4SXPMQN","bundle":"https://pith.science/pith/657P2WPD2RIOQHJMAWV4SXPMQN/bundle.json","state":"https://pith.science/pith/657P2WPD2RIOQHJMAWV4SXPMQN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/657P2WPD2RIOQHJMAWV4SXPMQN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:657P2WPD2RIOQHJMAWV4SXPMQN","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":"4d6a0d5b8fd7786df62f3d4d3b82f6e951e78d53a8be3d3204b7f0edd27e56d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-10T16:34:34Z","title_canon_sha256":"0ea97a872f005bb1b05d1005340925a080c4b77b142b90a7d7cfe0c32a1ed31c"},"schema_version":"1.0","source":{"id":"1405.2449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2449","created_at":"2026-05-18T01:09:42Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2449v1","created_at":"2026-05-18T01:09:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2449","created_at":"2026-05-18T01:09:42Z"},{"alias_kind":"pith_short_12","alias_value":"657P2WPD2RIO","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"657P2WPD2RIOQHJM","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"657P2WPD","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:387738863722b9b87b5e1c8d34e8fa2b1ede08f228602f7e9d84eb649c924ab8","target":"graph","created_at":"2026-05-18T01:09:42Z","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":"A strongly polynomial sequence of graphs $(G_n)$ is a sequence $(G_n)_{n\\in\\mathbb{N}}$ of finite graphs such that, for every graph $F$, the number of homomorphisms from $F$ to $G_n$ is a fixed polynomial function of $n$ (depending on $F$). For example, $(K_n)$ is strongly polynomial since the number of homomorphisms from $F$ to $K_n$ is the chromatic polynomial of $F$ evaluated at $n$. In earlier work of de la Harpe and Jaeger, and more recently of Averbouch, Garijo, Godlin, Goodall, Makowsky, Ne\\v{s}et\\v{r}il, Tittmann, Zilber and others, various examples of strongly polynomial sequences and","authors_text":"Andrew Goodall, Jaroslav Nesetril, Patrice Ossona de Mendez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-10T16:34:34Z","title":"Strongly polynomial sequences as interpretations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2449","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:a2c473385290e1bcd65452ef5c5bf2d280a2d2e2fe4637ceeba27589fad2d87b","target":"record","created_at":"2026-05-18T01:09:42Z","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":"4d6a0d5b8fd7786df62f3d4d3b82f6e951e78d53a8be3d3204b7f0edd27e56d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-10T16:34:34Z","title_canon_sha256":"0ea97a872f005bb1b05d1005340925a080c4b77b142b90a7d7cfe0c32a1ed31c"},"schema_version":"1.0","source":{"id":"1405.2449","kind":"arxiv","version":1}},"canonical_sha256":"f77efd59e3d450e81d2c05abc95dec837b9a88c0d5603d5b0e2030a39f87c26a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f77efd59e3d450e81d2c05abc95dec837b9a88c0d5603d5b0e2030a39f87c26a","first_computed_at":"2026-05-18T01:09:42.378243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:42.378243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3UdSCAcNgyXUMtq91dz+OW5wYjRje4BNz1dK2FoBxBLAVYSCYKGUB/sVIg3eaYDwWOU8UeEOjxCYoOr8J2phCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:42.378710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2c473385290e1bcd65452ef5c5bf2d280a2d2e2fe4637ceeba27589fad2d87b","sha256:387738863722b9b87b5e1c8d34e8fa2b1ede08f228602f7e9d84eb649c924ab8"],"state_sha256":"1a926858563b3c33d71c12976326c2fdf004f75e8e93d62dd4f549b7618b6cf1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmPmtsB6BIpT9DvPsnNv2n28GnJ72SE6dDnzUmXkTcxthDR9VE21MkSj9/dfjDgw58REw/p0hUoeQcj7a6xLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T08:26:06.444165Z","bundle_sha256":"25e77fba682bfb8522fd62e2f775eee4f3ac8ac2a5de1cf4b485109d499fd5c3"}}